Tutors Answer Your Questions about Geometry Word Problems (FREE)
Question 1198765: A flower garden is shaped like a circle. Its diameter is 38yd. A ring-shaped path goes around the garden. The width of the path is 5yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 7yd2, how many bags does the gardener need?
Click here to see answer by math_tutor2020(3816)  |
Question 1198871: A molasses can is made with a cylindrical base having a radius of 6
cm, that is topped by a smaller cylindrical pouring spout with radius
2 cm. When upright, the top of the molasses is 14 cm above the
base of the can, but when turned over, the top of the molasses is
19⅓ cm above the base. Find the total height of the can in cm.
Diagram of Molasses Can:
https://ibb.co/6RwWmPy
Click here to see answer by ikleyn(52778)  |
Question 1198876: A molasses can is made with a cylindrical base having a radius of 6
cm, that is topped by a smaller cylindrical pouring spout with radius
2 cm. When upright, the top of the molasses is 14 cm above the
base of the can, but when turned over, the top of the molasses is
19⅓ cm above the base. Find the total height of the can in cm.
Diagram of Molasses Can:
https://ibb.co/6RwWmPy
Ms.Ikelyn previously referred me to a solution by web2.0calc - however that solution is not valid as the poster did not provide a diagram as I have, hence, Cphil (answerer) had to make assumptions.
Click here to see answer by ikleyn(52778) |
Question 1198876: A molasses can is made with a cylindrical base having a radius of 6
cm, that is topped by a smaller cylindrical pouring spout with radius
2 cm. When upright, the top of the molasses is 14 cm above the
base of the can, but when turned over, the top of the molasses is
19⅓ cm above the base. Find the total height of the can in cm.
Diagram of Molasses Can:
https://ibb.co/6RwWmPy
Ms.Ikelyn previously referred me to a solution by web2.0calc - however that solution is not valid as the poster did not provide a diagram as I have, hence, Cphil (answerer) had to make assumptions.
Click here to see answer by math_tutor2020(3816) |
Question 1199078: A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? Use 3.14 to approximate pi. Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet)
I don't know how to do this problem. I simply followed a sample found on this website.
Let d = depth of the border
Let w = width of border to be found
Let V = volume of pool
Let r = radius of pool
V = d•pi(w + r)^2 - pi (25•d) = 27
V = 3•pi(w + 5)^2 - pi(25•3) = 27
V = 3•pi(w + 5)^2 - 75•pi = 27
Subtract 27 on both sides.
Set V = 0 and solve for w.
0 = 3•pi(w + 5)^2 - 75•pi - 27
After solving for w, I get two approximations:
-10.27871 and 0.278711
Of course, I must reject the negative value for w because distance must be positive.
The book's answer for the width of the border is 2.71 feet wide.
What am I doing wrong?
Thank you.
Click here to see answer by ikleyn(52778) |
Question 1199078: A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? Use 3.14 to approximate pi. Express your solution rounded to two decimal places. (1 cubic yard = 27 cubic feet)
I don't know how to do this problem. I simply followed a sample found on this website.
Let d = depth of the border
Let w = width of border to be found
Let V = volume of pool
Let r = radius of pool
V = d•pi(w + r)^2 - pi (25•d) = 27
V = 3•pi(w + 5)^2 - pi(25•3) = 27
V = 3•pi(w + 5)^2 - 75•pi = 27
Subtract 27 on both sides.
Set V = 0 and solve for w.
0 = 3•pi(w + 5)^2 - 75•pi - 27
After solving for w, I get two approximations:
-10.27871 and 0.278711
Of course, I must reject the negative value for w because distance must be positive.
The book's answer for the width of the border is 2.71 feet wide.
What am I doing wrong?
Thank you.
Click here to see answer by htmentor(1343)  |
Question 1199093: In the diagram, point N is on the inside of the cylinder, 10 cm from the bottom, and point M is on the outside of the cylinder, diametrically opposite Point N, 4 cm from the bottom. An ant walks from point M to point N, using the shortest possible route. The cylinder has height 12 cm and circumference 15 cm. When the ant got to the top of the cylinder, how many cm did it still have to walk? Ignore the thickness of the cylinder wall.
A) 3
B) 2
C) 2.25
D) 2.5
E) 2.75
https://ibb.co/XxKwJzQ
Click here to see answer by MathLover1(20849)  |
Question 1199113: The following problem is often used in textbooks using different measures.
An open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should be the dimensions of the shert metal?
Let me see.
I can label the length of a side of the square piece of metal as x.
The box will be of height 1 foot, and it's square base will measure (x - 2) on each side. The volume V of the box is V = (x - 2)(x - 2) • 1 or (x - 2)^2.
Is this right so far?
Click here to see answer by MathLover1(20849) |
Question 1199115: Last question for today.
The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in 4 : 3 format, meaning the ratio of the length to the width of the rectangular screen is 4 to 3. What is the area of a 37-inch Traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger?
Hint given but the textbook:
If x is the length of a 4 : 3 format screen, then (3x/4)is the width.
Let me see.
I know what x represents. I will say let y = length of a 16 : 9 format screen. If this is true, then 9y/16 is the width.
My set up for x goes like this:
37 = x(3x/4)
Solving for x, I get 7.024.
My set up for y goes like this:
37 = y(9y/16)
Solving for x,I get 8.11035.
I see that y > x,meaning the LCD TV screen format is bigger.
However, according to the textbook,I am wrong.
Textbook Answer:
The screen of a 37-inch TV in 4 : 3 format has an area of 657.12 in^2.
The screen of a 37-inch TV in 16 : 9 format has an area of 587.97 in^2.
According to the textbook, the traditional TV has the bigger screen.
Questions:
1. What did I do wrong?
2. What is the correct set up for each TV to find the area?
3. I have a hard time setting up the correct equation(s) leading to the right answer for most word problems. How can I improve my word problem-Solving skills?.
Thanks
Click here to see answer by ikleyn(52778) |
Question 1199115: Last question for today.
The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in 4 : 3 format, meaning the ratio of the length to the width of the rectangular screen is 4 to 3. What is the area of a 37-inch Traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger?
Hint given but the textbook:
If x is the length of a 4 : 3 format screen, then (3x/4)is the width.
Let me see.
I know what x represents. I will say let y = length of a 16 : 9 format screen. If this is true, then 9y/16 is the width.
My set up for x goes like this:
37 = x(3x/4)
Solving for x, I get 7.024.
My set up for y goes like this:
37 = y(9y/16)
Solving for x,I get 8.11035.
I see that y > x,meaning the LCD TV screen format is bigger.
However, according to the textbook,I am wrong.
Textbook Answer:
The screen of a 37-inch TV in 4 : 3 format has an area of 657.12 in^2.
The screen of a 37-inch TV in 16 : 9 format has an area of 587.97 in^2.
According to the textbook, the traditional TV has the bigger screen.
Questions:
1. What did I do wrong?
2. What is the correct set up for each TV to find the area?
3. I have a hard time setting up the correct equation(s) leading to the right answer for most word problems. How can I improve my word problem-Solving skills?.
Thanks
Click here to see answer by MathTherapy(10551)  |
Question 1199115: Last question for today.
The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in 4 : 3 format, meaning the ratio of the length to the width of the rectangular screen is 4 to 3. What is the area of a 37-inch Traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger?
Hint given but the textbook:
If x is the length of a 4 : 3 format screen, then (3x/4)is the width.
Let me see.
I know what x represents. I will say let y = length of a 16 : 9 format screen. If this is true, then 9y/16 is the width.
My set up for x goes like this:
37 = x(3x/4)
Solving for x, I get 7.024.
My set up for y goes like this:
37 = y(9y/16)
Solving for x,I get 8.11035.
I see that y > x,meaning the LCD TV screen format is bigger.
However, according to the textbook,I am wrong.
Textbook Answer:
The screen of a 37-inch TV in 4 : 3 format has an area of 657.12 in^2.
The screen of a 37-inch TV in 16 : 9 format has an area of 587.97 in^2.
According to the textbook, the traditional TV has the bigger screen.
Questions:
1. What did I do wrong?
2. What is the correct set up for each TV to find the area?
3. I have a hard time setting up the correct equation(s) leading to the right answer for most word problems. How can I improve my word problem-Solving skills?.
Thanks
Click here to see answer by math_tutor2020(3816) |
Question 1199114: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide will the border be?
Without going into too much detail, in this website I found that someone answered the question by coming up with the following equation:
(2x + 6) (2x + 10) = 168
Let x = width of the border.
My question is:
Where did 168 come from?
Thanks.
Click here to see answer by ikleyn(52778) |
Question 1199273: Points B(b,0) and C(c,10) are to be placed on this graph so that the distance from A to B to C to D is a minimum. Find the value of b.
Also: Point A is at (0,4) and point D is at (8,9)
PLEASE DO NOT GIVE ME THE SOLUTION OF MATHLOVER AS IT IS INCORRECT. HER ANSWER IS NOT ONE OF THE MULTIPLE CHOICE WHICH CAN BE FOUND HERE:
a) 3 4/15
b) 1 7/15
c) 2 2/25
d) 2 4/15
e) 2 7/15
Thanks!
Click here to see answer by Alan3354(69443)  |
Question 1199273: Points B(b,0) and C(c,10) are to be placed on this graph so that the distance from A to B to C to D is a minimum. Find the value of b.
Also: Point A is at (0,4) and point D is at (8,9)
PLEASE DO NOT GIVE ME THE SOLUTION OF MATHLOVER AS IT IS INCORRECT. HER ANSWER IS NOT ONE OF THE MULTIPLE CHOICE WHICH CAN BE FOUND HERE:
a) 3 4/15
b) 1 7/15
c) 2 2/25
d) 2 4/15
e) 2 7/15
Thanks!
Click here to see answer by greenestamps(13198)  |
Question 1199275: Points B(b,0) and C(c,10) are to be placed on this graph so that the distance from A to B to C to D is a minimum. Find the value of b.
Also: Point A is at (0,4) and point D is at (8,9)
I'd like to thank MathLover for a solution to this problem previously. However, I cannot find her answer in the multiple choice that I was given. Please let me know what is going on.
a) 3 4/15
b) 1 7/15
c) 2 2/25
d) 2 4/15
e) 2 7/15
Thanks!
Click here to see answer by ikleyn(52778) |
Question 1199340: A hot-air balloon is flying at an altitude of 2687 feet. If the angle of depression from the pilot in the balloon to a house on the ground below is 26, find the distance from the hot air balloon to the house.
Click here to see answer by ikleyn(52778) |
Question 1199540: 3) To find the height of a tower, a surveyor positions a measurement device that is 2 m tall at a spot 24 m from the base of the tower. She measures the angle from the top of the measurement device to the top tower to be 45°. What is the height of the tower? Show your work.
Click here to see answer by math_tutor2020(3816) |
Question 1199598: Ms.Ikelyn, for the solution you gave for the problem here:
https://www.algebra.com/tutors/students/your-answer.mpl?question=1199595
Doesn't make sense to me. Because if we subtract the area of the large circle and the small circles, the difference is more than just the "a" regions. Please let me know how to overcome this obstacle. Thanks!
Click here to see answer by math_tutor2020(3816) |
Question 1199587: Alpha particles are deflected along the hyperbolic paths when they
are directed towards the nuclei of gold atoms. If an alpha particle
gets as close as 12 units to the nucleus along the hyperbolic path
with asymptotes of 𝑦=5x/12, what is the equation of its path.
Assume that the transverse axis is on y-axis. Illustrate the said path
taken by the alpha particles. Illustrate the path taken by the alpha
particles.
Click here to see answer by ikleyn(52778) |
Question 1199586: Alpha particles are deflected along the hyperbolic paths when they
are directed towards the nuclei of gold atoms. If an alpha particle
gets as close as 12 units to the nucleus along the hyperbolic path
with asymptotes of 𝑦=5x/12, what is the equation of its path.
Assume that the transverse axis is on y-axis. Illustrate the said path
taken by the alpha particles. Illustrate the path taken by the alpha
particles.
Click here to see answer by ikleyn(52778) |
Question 1199630: The number of pairs of integers (x,y) that satisfy both x^2 + y^2 ≤ 36 and y= -4 is...?
a) 4
b) 5
c) 6
d) 7
e) 8
This solution here: https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1064755.html
By Ms.Ikelyn didn't make sense to me if she could elaborate. Also, I couldn't find 9 in the multiple choice. Thank you so much!
Click here to see answer by ikleyn(52778) |
Question 1199630: The number of pairs of integers (x,y) that satisfy both x^2 + y^2 ≤ 36 and y= -4 is...?
a) 4
b) 5
c) 6
d) 7
e) 8
This solution here: https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1064755.html
By Ms.Ikelyn didn't make sense to me if she could elaborate. Also, I couldn't find 9 in the multiple choice. Thank you so much!
Click here to see answer by math_tutor2020(3816) |
Question 1199693: A child sees a bird in a tree. The child’s eyes are 4 ft above the ground and 12 ft from the bird. The child sees the bird at the angle of elevation of 40o. What is the bird’s approximate height above the ground?
Click here to see answer by ikleyn(52778) |
Question 1199792: The cross section of a window box planter is an isosceles trapezoid with the area of 96 square inches. The bases of the cross section have lengths of 10 inches and 14 inches. What is the height, in inches, of the planter?
Click here to see answer by ikleyn(52778) |
Question 1199890: A total of $7000 is deposited into two simple interest accounts. In one account the annual simple interest rate is 3%, and in the second account the annual simple interest rate is 7%. The amount of interest earned for 1 year was $250. How much was invested in each account?
Click here to see answer by math_tutor2020(3816) |
Question 1199892: A jeweler wants to make a silver alloy to be used to make necklaces. How many ounces of a silver alloy that costs $4.50 per ounce should be mixed with one that costs $9.00 per ounce to make a new 30-ounce alloy that costs $8.10 per ounce?
Click here to see answer by josgarithmetic(39617) |
Question 1199889: An investment adviser invested $14,000 in two accounts. One investment earned 5% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $535. How much was invested in each account?
Click here to see answer by ikleyn(52778) |
Question 1199921: Mr.Greenstamps posted a problem here:
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1134175.html
Also, the original image link has expired, so here it is again for your reference: https://ibb.co/yNfgt93
I would like some help understanding Mr.Greenstamps' solution.
Firstly, I don't really understand the 4 units forward ("F"), 4 units left (L"), and 4 units down ("D"). The "4 units down" in particular.
Here's a diagram I made:
https://ibb.co/qNnw2Bn
Clearly, you can see that from A, you can only move UP, LEFT, or FORWARD. Perhaps my intuition here is wrong, but I'm not sure. Please let me know.
Thanks!!
Click here to see answer by greenestamps(13198) |
Question 1199921: Mr.Greenstamps posted a problem here:
https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1134175.html
Also, the original image link has expired, so here it is again for your reference: https://ibb.co/yNfgt93
I would like some help understanding Mr.Greenstamps' solution.
Firstly, I don't really understand the 4 units forward ("F"), 4 units left (L"), and 4 units down ("D"). The "4 units down" in particular.
Here's a diagram I made:
https://ibb.co/qNnw2Bn
Clearly, you can see that from A, you can only move UP, LEFT, or FORWARD. Perhaps my intuition here is wrong, but I'm not sure. Please let me know.
Thanks!!
Click here to see answer by ikleyn(52778) |
|
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020
|
