Tutors Answer Your Questions about Circles (FREE)
Question 571361: how do you find the are of a circle that has lines on it and has a square around it on a coordinate plane. =a(-2,3), B (6,3), c (6,-5), D (-2,-5)
Answer by solver91311(12118)   (Show Source):
Question 571232: A park has just installed a circular fountain in 8 meters diameter. The park wants to pave a 1.5 meter wide path around the fountain. If paving costs 10 dollars per square meter, find the cost to the nearest dollar of the paved path around the fountain.
Answer by Theo(2967)  (Show Source):
You can put this solution on YOUR website!fountain is 8 meters in diameter.
this makes the radius equal to 4 meters.
add 1.3 meters to make the radius of the outer edge of the path around the fountain equal to 5.3 meters.
the area of the fountain is pi*r^2 = pi*4^2 = 16*pi square meters.
the area of the path plus the fountain is pi*r^2 = pi*5.3^2 = 28.09*pi square meters.
the difference between the larger area and the smaller area is the area of the path around the fountain.
this is equal to 28.09*pi - 16*pi which is equal to 12.09*pi square meters.
if you multiply this by $10.00 a square meter, then you get a total cost of $120.9 * pi dollars.
this results in $379.818 dollars which rounds to $380 dollars.
the diagram shows how this was done.
Question 570866: area: 3.14 or 22/7
diameter is 29ft
Answer by JBarnum(1826)  (Show Source):
Question 570393: The circumference of a plate is 18.84 inches.
What is the diameter of the plate?
Answer by rfer(10417) (Show Source):
Question 570373: The shaded sector of the circle above covers of the circle. If the radius of the circle is 20 cm, what is the approximate area of the shaded sector?
Answer by stanbon(48516) (Show Source):
Question 567951: please help :
the measure of a central angle of a sector is 36 degrees. the arc length of the sector is 4pi cm. what is the radius of the circle.
Answer by josmiceli(6778)  (Show Source):
Question 567929: Identify one (1) lesson on circles that you would deliver to your students and explain how you could integrate the Seed of Life in the delivery of the lesson.
Answer by richard1234(4789)  (Show Source):
You can put this solution on YOUR website!Teach something about circles and how to construct circles using a compass, using the Seed of Life as a practice. Teach about the symbolism involved with this pattern.
Question 567738: Please help me solve:
The arc length of a sector is 5pi cm. If the circle has a radius of 9cm, what is the measure of the central angle of the sector?
Answer by Alan3354(21555)  (Show Source):
You can put this solution on YOUR website!The arc length of a sector is 5pi cm. If the circle has a radius of 9cm, what is the measure of the central angle of the sector?
----------
Angle = 5pi/9 radians
Question 567726: The area of a 60 degree sector of a circle is 36pi cm^2. What is the diameter of the circle?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!The area of a 60 degree sector of a circle is 36pi cm^2. What is the diameter of the circle?
--------------
1/6 of the circle has an area of 36pi
The whole circle's area = 216pi
 cm
Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!The area of a 60 degree sector of a circle is 36pi cm^2. What is the diameter of the circle?
That sector has 1/4 of the total area of the circle.
---
Area of the circle = 4(36pi) = 144pi
-----
Area = (pi)r^2
----
Equation:
(pi)r^2 = 144pi
r^2 = 144
r = 12
-------
Diameter = 2r = 24 cm
=================================
Cheers,
Stan H.
==================
Question 566196: A circle has a radius of 4 centimeters what is the circumference and area of the circle
Answer by Alan3354(21555) (Show Source):
Question 565432: If a flagpole measures 19 1/16 inches around, what is the diameter of the flagpole?
Answer by Alan3354(21555) (Show Source):
Question 564699: Explain (suggested length 1–2 paragraphs) how the functions and definitions in parts A1 and A2 are related by investigating a right triangle inscribed in a unit circle. Refer to the diagrams in parts A1 and A2 as necessary.
a. Explain how you remember the relationships among these trigonometric functions.
part a1 refers to the right triangle definitions in this completed chart
part a2 refers to the unit circle definitions
Function Right Triangle Definition Unit Circle Definition
Sine Opposite/hypotenuse Sin (ang+ 2 pi k)
Cosine Adjacent/hypotenuse Cos (ang+ 2 pi k)
Tangent Opposite/adjacent Sin/cos
Cosecant Hypotenuse/side opposite acute angle
Reciprocal of sine 1/sin
Secant Hypotenuse/short side adjacent to acute angle
Reciprocal of cosine 1/cos
Cotangent Side adjacent to acute angle/side opposite angle 1/tan or sin/cos
Answer by richard1234(4789) (Show Source):
You can put this solution on YOUR website!You didn't provide any diagrams. I think you are referring to a triangle that looks something like this:
Suppose that this triangle is part of the unit circle with radius 1 and origin O(0,0). Then
 = \frac{opp}{hyp} = \frac{a}{1} = a)
 = \frac{adj}{hyp} = \frac{b}{1} = b)
Other trig functions (tan, csc, etc.) should follow. Note that b and a are simply the x- and y-coordinates of a point on the unit circle.
Question 564250: what is the radius of a circle when the center is at (3,5) and it passes through the origin?
Answer by TutorDelphia(189)  (Show Source):
You can put this solution on YOUR website!To find the radius you need a point along the circle and the center. The center is (3,5) the point along the circle is the origin (0,0)
We can use distance formula to solve from here, and the zeros will make this easy
Question 564130: Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?
Answer by richard1234(4789) (Show Source):
Question 563793: The larger circle circumscribes an equilateral triangle, which circumscribes a small circle. The area of the larger circle is 12pi. What is the triangle's perimeter. I not sure how to do this problem and how to work it out.
Answer by Theo(2967) (Show Source):
You can put this solution on YOUR website!i can solve this using trigonometry
i don't know how to solve it otherwise,
using trigonometry i would do the following:
the area of the larger circle is equal to 12*pi
since the area of a circle is equal to pi*r^2, this means that:
the radius of the circle = sqrt(12)
the radii of the big circle in the diagram are:
DB, DC, DA
the radii of the small circle in the diagram are:
DE, DF, DG
these radii are also the apothems of the triangle.
the apothems of the triangle intersect the sides of the triangle at a right angle.
this forms 8 right triangles.
they are:
DBF, DFC, DCG, DGA, DAE, DEB
the hypotenuse of each of these 8 triangles are the radii of the large circle.
this makes their length equal to sqrt(12)
the angle of each of these triangles with a vertex at the center of the circle is equal to 60 degrees.
using trigonometry, you can calculate the distance of the legs of these triangles that form the perimeter of the larger triangle which is an equilateral triangle and is labeled ABC.
using right triangle DBF:
the hypotenuse is DB with a length of sqrt(12)
the angle is BDF which is 60 degrees.
the sine of angle BDF is equal to opposite / hypotenuse which is equal to BF / BD
since BD is equal to sqrt(12), then we get:
sine (BDF) is equal to BF / sqrt(12)
multiply both sides of this equation by sqrt(12) to get:
BF = sqrt(12) * sine(BDF)
since angle BDF is 60 degrees, we get:
BF = sqrt(12) * sine (60) which becomes:
BF = 3
2 * 3 is equal to the length of one of the sides of the equilateral triangle.
3 * 2 * 3 is equal to the perimeter of the equilateral triangle.
that perimeter is equal to 18.
the diagram is shown below:
Question 563559: How do you find the four vertex of a square of length 283 inscribed in a circle with a radius of 200??
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!How do you find the four vertex of a square of length 283 inscribed in a circle with a radius of 200??
--------
What is a "square of length 283" ?
Question 563205: what is the area of a circle in terms of pie, and they give you 3/4 in.
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(12118) (Show Source):
You can put this solution on YOUR website!
So what is 3/4 inch? The radius? The diameter? The circumference?
The area of a circle is given by
Where  is the radius. If instead you have the diameter, then  . If instead you have the circumference, then 
By the way, "pie" is generally considered to be a food item, with one or more more or less flaky pastry crusts and containing some sort of filling. Pies served for dessert generally contain some sort of sweet filling, such as a prepared mixture of fruit and sugar, or perhaps some sort of sweet pudding-like substance. Pies served as either side or main dishes generally have some sort of savory filling that primarily features some sort of meat. "pi" is the generally accepted romanization of the lower case Greek alphabetic character  that, in a mathematics context, is recognized to stand for the trancendental irrational constant that is the ratio between the diameter and the radius of a circle.
John
My calculator said it, I believe it, that settles it
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!what is the area of a circle in terms of pie, and they give you 3/4 in.
------
Is 3/4 in. the radius? The diameter? The circumference? The distance to somewhere?
Question 560986: If the Circumference equals 5(3.14) cm, find the diameter
Answer by richard1234(4789) (Show Source):
Question 560480: What is the measure of the smaller angle formed by the hour and minute hands at 1:28? Please explain.
Answer by TutorDelphia(189) (Show Source):
You can put this solution on YOUR website!On a traditional clock, the clock's hours are divided into 12 equal segments and the minutes into 60
so at 1:28 the hour hand is 1/12 of the way around and the minute hand is 28/60 of the way around. We can convert both into degrees by multiplying by 360, the number of degrees in a circle
(1/12)*360=30
(28/60)*360=168
To find the angle, just find the difference between the two degrees. 168-30=138
Question 560343: Please help me solve this :
A semi Circle has a diameter of 20.9cm
Work out the perimeter of the semi circle
Give your answer to an appropriate degree of accuracy.
Now i know you have to do pi * diameter,
SO - 3.142 *20.9 = 65.67
Answer by stanbon(48516) (Show Source):
You can put this solution on YOUR website!SO: 3.142 *20.9 = 65.67
----
That is the perimeter of the whole circle.
You want half of that.
You also need the base of the semi-circle, which is the diameter.
---
Perimeter = (65.67/2) + 20.9 = 53.74
==================
Cheers,
Stan H.
==================
Question 560036: if the radius is 15 and pi is 6 what is the central angle?
Answer by Alan3354(21555) (Show Source):
Question 559534: I am asked to: Find the equation of each circle. Express my answer in general form.
i am given:
Center (5,-3) and radius of 2root2
i know i am suppose to use
(x-h)^+(y-k)^=r^ ... but having trouble completing the square
Answer by richard1234(4789) (Show Source):
Question 558817: If the endpoints of a circle's diameter are (6, 2) and (0, –6), what is the area of the circle?
Answer by rapaljer(4551)  (Show Source):
You can put this solution on YOUR website!Distance between the two end points is the diameter of the circle.
 units
 units
Area = 
Area = 
Area =  square units
For additional examples and explanation on Circles, please see my website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.
Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", and look in "Chapter 2," Section 2.04 Circles for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR.
Everything on the website is FREE. If you find something you really like, just print your own copy of it!!
If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 558412: I have a question for my homework that I never learned, and I was wondering if it could be explained to me.
If the area of a circle is 25 meters, what is its radius in meters?
Answer by rfer(10417) (Show Source):
Question 558049: A diameter of a circle has endpoints at (4, 6) and the origin. Which point is also on the circle?
A. (–1, 2) B. (6, 3) C. (5, 0) D. (–1, 1) E. NOTA
Please explain.
Answer by solver91311(12118) (Show Source):
Question 557803: find the area of the largest circle which can be cut from a square with an edge of 8cm.what is the area of the materials wasted?
Answer by Edwin McCravy(6932)  (Show Source):
You can put this solution on YOUR website!
 
As you can see the green line segment is the diameter of the circle and it
is the same length as the edge of the square, so the diameter of the circle
is also 8 cm. Since the radius of the circle is one-half of the diameter
the radius of the circle is 4cm.
Area of square = side² = (8cm)² = 64 cm²
Area of circle = pr² = (3.14)(4cm)² = (3.14)(16cm²) = 50.24 cm²
Area of waste = Area of square - Area of circle = (64 cm²)-(50.24 cm²) = 13.76 cm²
Edwin
Question 557774: 1. two parallel lines touch the circle at points A and B respectively. if area of the circle is 25pie cm2. then AB is equal to?
2. Area of the greatest circle of the circles constructed on the side of a right triangle, taking these sides as diameters, if the two smalles sides are 1.5cm and 2cm.
Answer by mananth(10541)  (Show Source):
You can put this solution on YOUR website!Area = 25 pi cm^2
AB are on lines parallel to each other
so AB is the diameter
Area = pi*r^2
25 pi = pir^2
r^2=25
r= 5 cm
AB = 10 cm
-------------
Hypotenuse ^2= leg1^2+leg2^2
leg1 = 1.5 cm
Leg2^2= 2 cm
Hypotenuse^2 1.5 ^2 + 2 ^2
Hypotenuse^2 2.25 + 4
Hypotenuse^2 6.25
take the square root
Hypotenuse^2 2.5 cm
the diameter of the circle = 2.5 cm
radius = 1.25
Area of circle = pi*r^2
Area =pi*1.25^2
Area = 4.90 cm^2
----------
Question 557522: The manager of a sandwich shop is planning to make a circle graph showing the types of sandwiches sold in one day. The table below summarizes these data.
Sandwiches Sold in One Day
Roast beef
195
Turkey-and-cheese
125
Ham-and-cheese
75
Vegetable
50
Other
55
What central angle should the manager use for the section representing the ham-and-cheese sandwich?
Answer by neatmath(225)  (Show Source):
You can put this solution on YOUR website!Without actually drawing the graph, we can find this answer.
Add up the total amount of sandwiches sold:
Conveniently, the store sold 500 sandwiches.
Now we just need to compare the number of ham and cheese sandwiches sold (75),
to the total number of sandwiches sold (500) to get a ratio:
Now, since a circle has a total of 360 degrees in it, if we multiply our ratio R by 360,
we will know the measure of the central angle that the ham and cheese sandwiches should have on the graph.
So the ham and cheese central angle on the graph should be 54 degrees.
If we were using radians, of course we would have a different answer, but the process would be exactly the same.
We would just need to multiply our ratio R by 
 which would be the exact answer in radians.
I hope this helps! :)
*******************************************************
Email Scott King: neatmath@yahoo.com for help with specific problems,
or to inquire about low-cost mathematics tutoring via email or other methods.
Paypal is always accepted for detailed assistance with single problems.
Single problems would range from 50 cents to 5 dollars each, depending on their complexity.
Question 557433: The length of a tangent from point A at distance 5 cms from the center of the circle is 4 cm. Find the radius of the circle.
Answer by rajagopalan(148)  (Show Source):
You can put this solution on YOUR website!The length of a tangent 4
A at distance 5 cms from the center of the circle
Let Radius =R
Tangent meant it makes 90 degrees
so 4square+R square=5 square
4^2+R^2=25
R^2=25-16
R^2=9
R=root9
R=3
Rad of circle=3 units
Question 555696: What is the circumference and area of a circle that has a radius of 4”?
Answer by Alan3354(21555) (Show Source):
Question 555290: what is the circumfrence of a 12-inch pizza
Answer by jim_thompson5910(21667) (Show Source):
Question 555063: what is the equation of a circle with center (-6,4) passing through the points (9,4).?
Hope to hear from you soon.
Thank you and Godbless!
I promise to pay your kindness in any way that i can.
Answer by KMST(578)  (Show Source):
You can put this solution on YOUR website!The radius is the distance between the two points given.
They have the same y coordinate, so the distance is the difference between the x coordinates 
A circle is the collection of all the points at a certain distance from the center point.
Your circle is the collection of all the points at a distance of 15 from the center point (-6, 4).
The distance squared would be  .
The square of the distance from a point (x, y) to (-6, 4) is
 .
If that point is in the circle of the problem,
 .
That equation is the equation of the circle with center (-6,4) passing through the points (9,4). If a point is in that circle its coordinates will satisfy that equation. If the coordinates of a point satisfy that equation, the point is in the circle.
Question 555068: what is the center and radius of A Circle whose equation is x^2+8x+y^2-10y+32=0 ?
Hope to hear from you soon.
Thank you and Godbless!
I promise to pay your kindness in any way that i can.
Answer by htmentor(580)  (Show Source):
You can put this solution on YOUR website!what is the center and radius of A Circle whose equation is x^2+8x+y^2-10y+32=0 ?
==================
Complete the squares:
x^2 + 8x -> (x+4)(x+4) = x^2 + 8x + 16
y^2 - 10y -> (y-5)(y-5) = y^2 -10y + 25
The constant terms add up to 41: 41 - 9 = 32
So the equation of the circle is:
(x+4)^2 + (y-5)^2 = 9
Center at (-4,5), radius = 3
Question 554607: An eighteen inch pizza arrived at a boys table. The crust was one inch wide all the way around the pizza. What percent of the pizza is crust?
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!An eighteen inch pizza arrived at a boys table. The crust was one inch wide all the way around the pizza. What percent of the pizza is crust?
----------
The outside radius is 9, the inside is 8 inches
It's a function of the square of the radius.
(8^2/9^2) = 64/81 is the inside
17/81 is the crust
==~ 21% is the outside crust.
Question 554248: r=8inch put your answers in terms of pi
Found 2 solutions by rapaljer, stanbon:
Answer by rapaljer(4551) (Show Source):
You can put this solution on YOUR website!What do you want to find?
 inches
 square inches
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Answer by stanbon(48516) (Show Source):
Question 554129: what is the center and radius of the equation below?
x^2+y^2-8x-2y+16=0
Answer by rapaljer(4551) (Show Source):
You can put this solution on YOUR website!Complete the square on this one. First, get the x terms together and the y terms together, leaving a blank to add to the x terms and y terms in order to complete the square. Place similar blanks on the right side so you can add numbers to BOTH sides of the equation, as follows:
x^2 -8x + ____ + y^2 -2y + _____ = -16 + ____ + ____
Take half of the -8, which is -4, and square, which would be 16.
Take half of the -2, which is -1, and square, which would be 1. Fill in the blanks above with these numbers, adding the numbers to each side of the equation.
x^2 - 8x + 16 + y^2 - 2y + 1 = -16 +16 +1
(x-4)^2 + (y-1)^2 = 1
Therefore the center is at (4,1), and the r^2=1, so the radius is 1.
You may want to see my FREE website for a non-traditional explanation of this topic. The easiest way to find the website is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. Near the bottom of this page is a link that takes you to my Homepage.
On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra" and look in "Chapter 2" for "Section 2.04 Circles." I think you will really like the "Math in Living Color" pages that go with this section.
If you need to contact me, send me an Email at rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 553984: This is a personal question, just wondering how i could solve it, however i will accept an answer.
If a beehive makes crops take less time to get to a harvesting stage, and a beehive covers a Circle with a radius of 13 Meters. How large of a square could i put inside of the Circle so that the most crop area was covered? I thought it would be 18 Meters x 18 meters, but it doesn't seem to work. Any Ideas?
Found 2 solutions by Theo, Alan3354:
Answer by Theo(2967) (Show Source):
You can put this solution on YOUR website!circle has a radius of 13 meters which means that the diagonal of a square that is inscribed in the circle will be 26 meters.
this means that a side of the square will be equal to 18.38477631
this means that the crop area to be covered will be 18.38477631^2 = 338 square meters.
the area of the circle itself will be equal to pi*r^2 = pi*13^2 = 530.9291585 square meters.
a picture of what i believe you are asking about is shown below:
the sides of the square and the diagonal of the square form a right triangle.
in a right triangle, the hypotenuse is equal to the sum of the squares of each leg.
if you let s = the length of each leg, then you get:
s^2 + s^2 = 26^2 which gets you:
2s^2 = 676
divide both sides of this equation by 2 gets you:
s^2 = 338
take the square root of both sides of this equation to get:
s = 18.38477631
you were close but no cigars for you this time unless i misunderstood the problem.
Answer by Alan3354(21555) (Show Source):
You can put this solution on YOUR website!If a beehive makes crops take less time to get to a harvesting stage, and a beehive covers a Circle with a radius of 13 Meters. How large of a square could i put inside of the Circle so that the most crop area was covered? I thought it would be 18 Meters x 18 meters, but it doesn't seem to work. Any Ideas?
---------------
The diagonal of the square is the diameter of the circle, = 26 meters.
The sides of the square = 
s =~ 18.385 meters
Question 554037: Given:
Radius OR is perpendicular to chord AB at C
AC=2(x-3), BC=x+8
Find: AC, BC, and AB
Answer by Earlsdon(6098) (Show Source):
You can put this solution on YOUR website!If the radius, OR, is perpendicular to chord AB, then it bisects AB so that AC = BC.
2(x-3) = x+8 Solve for x.
2x-6 = x+8
x = 14 so...
AC = 2(x-3) = 2(14-3) = 22.
BC = x+8 = 14+8 = 22.
AB = AC + BC = 22+22 = 44.
Question 553370: A circle and a semicircle have the same area. If the circle has radius 1, what is the radius of the semicircle?
Answer by rapaljer(4551) (Show Source):
You can put this solution on YOUR website!Area of a circle: 
If r=1, then 
Area of a semicircle 
Since the area of the semicircle is the same as the area of the circle,  .
Multiply both sides by 2 to clear the fraction:
Divide both sides by pi:
 or  Reject the negative answer since a radius cannot be negative.
Final Answer!!
Happy New Year!! My Email address is rapaljer@seminolestate.edu if you need to contact me!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 552458: in a certain cake two straight cuts succeed in removing 4/15of the cake.waht is the central angle in degrees of the piece cut?
Answer by JBarnum(1826) (Show Source):
Question 552487: If a chord 10 inches long is 5 inches from the center of a circle, find the radius of the circle.
x =
Answer by vleith(2517) (Show Source):
You can put this solution on YOUR website!draw a circle and then draw a chord. Mark that chord as lenght 10.
The closest point of that chord to the center of the circle is the midpoint of the chord.
Draw a radius from the center of the circle through the midpoint of the chord.
Label the length from the center to the midpoint as 5.
Label the length from the point where the chord touches the circle to the midpoint as 5 (the chord lenght is 10. So half of that is 5)
Draw two radii from the center of the circle to the points where ends of the chord touches the circle.
Label those radii as R.
You now have right triangles with sides of 5 and 5. And a hypoteneus of length R.
Use the pathagorean theorem to solve for R 
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