# Questions on Geometry: Bodies in space, right solid, cylinder, sphere answered by real tutors!

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 Geometry: Bodies in space, right solid, cylinder, sphere Solvers Lessons Answers archive Quiz In Depth

Question 749935: A large cube, 5cm by 5cm by 5cm is painted orange an all six faces, and then it is cut into 125 small cubes, each 1cm by 1cm by 1cm. How many of the small cubes are not painted orange on any face?
(a)125
(b)64
(c)27
(d)24
(e)9

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This is a giant cube made of 125 small cubes, 5x5x5.
The inner 3x3x3 cube has one layer covering it from any paint, so these cubes are paint-free, 3x3x3 is 27.

Question 747989: A trucks wheel has a diameter of 1 m and a cars wheel is half this. How many times does the trucks wheel turn in 1 kilometer ? Predict how many times the cars wheel turns in one kilometer.
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A trucks wheel has a diameter of 1 m and a cars wheel is half this. How many times does the trucks wheel turn in 1 kilometer ?
It moves m per rev
# of revolutions = 1000/pi
-------
Predict how many times the cars wheel turns in one kilometer.
We don't predict, we calculate.
2x as many = 2000/pi

Question 747351: If I took a plain sheet of paper (8 1/2 x 11") and folded it to make a cylinder length wise and then width wise, which cylinder would have the most volume.
Found 2 solutions by josgarithmetic, Alan3354:
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Lengthwise: 2*pi*r=8&1/2
r=(8&1/2)/(2*pi)
volume=pi*r^2*11
volume=pi*((8&1/2)/(2*pi))^2*11
volume=
which is smaller than widthwise way.

Widthwise: 2*pi*r=11
r=11/(2*pi)
volume=pi*r^2*(8&1/2)
volume=pi*(11/(2*pi))^2(8&1/2)
volume=
, which is bigger than the lengthwise way.

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If I took a plain sheet of paper (8 1/2 x 11") and folded it to make a cylinder length wise and then width wise, which cylinder would have the most volume.
---------------
Vol of the taller cylinder = pi*4.25^2*11
Vol of the shorter one = pi*5.5^2*8.5
Compare them.

Question 746738:
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Question 736378: If radius of a sphere is doubled how many times its volume is increased
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The volume of a sphere is V =*
r is doubled: = 8 times

Question 734820: suppose you double the radius of a right cylinder
a how does that affect the lateral area?
b how does that affect the surface area?

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suppose you double the radius of a right cylinder
a how does that affect the lateral area?

r^1 --> 2x the Lateral Area
--------
b how does that affect the surface area?
Area of ends = pi*r^2
r^2 --> 4x the area of the ends
The total surface area is the sum of the LA and the 2 ends
-----------------

Question 730292: A cylinder of radius of 10cm. It already contains water to depth of 15cm. A metal sphere with volume 900cm^3 is placed in the water. Calculate the height that the water level rises
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A cylinder of radius of 10cm.
It already contains water to depth of 15cm.
A metal sphere with volume 900cm^3 is placed in the water.
Calculate the height that the water level rises
:
Find the vol of water in the cylinder
V =
V =
V = 4712.4 cu/cm of water
:
Find the total volume of the water and the sphere
4712.4 + 900 = 5612.4 cu/cm
:
Find the height (h) of the water when displaced by the sphere
= 5612.4
h =
h = 17.8647 cm is the height
:
;
Check this by finding the vol of the water between 17.8647 - 15 = 2.8647cm
V =
V = 899.97 ~ 900, the vol of the sphere

Question 727397: a billiard ball is inscribed in a plastic cubical box having a volume of 2744 mm^3. what is the ratio of the billiard ball to that of the volume of the plastic cubical box
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The diameter of the ball is the same as the width of the box, and 2 times the radius.
The formula for volume of a sphere says that a ball of the radius
has a volume of

A cube-shaped box of inside width has an inside volume of

The ratio of the volumes is
--> -->
The sizes of ball and box do not matter.
As long as the ball fits tightly in the box, and the box is cube-shaped, the ratio is the same.

NOTE:
If you are curious, and that would make the diameter of your billiard ball 14mm.
That is way too small, marble size.
I did not use a calculator to find

I just divided 2744 by 2, by 2, by 2, and by 7 to get 49 and realize that the prime factorization is

so I knew that

Question 718108: How long wold it take a sample of Am-241 to reduced to 25% of its original value?
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How long wold it take a sample of Am-241 to reduced to 25% of its original value?
-------------------
Two (2) times its half-life.

Question 714551: How many gallons are in a cylinder with a diameter of 8.5 inches and height of 8.5 inches?
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How many gallons are in a cylinder with a diameter of 8.5 inches and height of 8.5 inches?
-------------
r = d/2
cubic inches
convert to gallons

Question 712399: What is the volume of a cylinder
height = 7cm, using pi = 3.1?

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What is the volume of a cylinder
height = 7cm, using pi = 3.1?
----
Volume = (area of base)(height)
---
V = (3.17*6^2)(7)
V = 798.84 cu. cm.
=======================
Cheers,
Stan H.
=======================

Question 704571: The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the cylinder are also the same and are twice the length of the radius. If two cones are formed within the cylinder, as shown in the diagram, then the volume of the sphere is equal to which of the following?
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The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the cylinder are also the same and are twice the length of the radius. If two cones are formed within the cylinder, as shown in the diagram, then the volume of the sphere is equal to which of the following?
---------------
There's no diagram, and nothing follows.

Question 702749: an indoor roller skating rink with an area of 1500 sq yd. has a concrete flooring 3 in. thick. Find the amount of concrete used in laying the floor.
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an indoor roller skating rink with an area of 1500 sq yd. has a concrete flooring 3 in. thick. Find the amount of concrete used in laying the floor.
-------------
Vol = Area * depth
Vol = 1500 sq yd * 9 sq ft/sq yd * 3 inch * 1 ft/12 inch
Vol = 3375 cubic feet

Question 701067: the size of a brick is 25 cm by 12 cm by 55 cm and its density is the 1.8 by 10^3 kg/m^3.how many trips must a 3 ton dumper carry out to transport 15000 bricks to a constrution site?

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Volume of brick = 0.25m * 0.12m * 0.55m = 0.0165 cu.m
volume of 1 brick = 0.0165 cu.m
density = 1.8*10^3 kg/m^3
weight of 1 brick = 0.0165* 1.8*10^3
29.7 kg
15000 bricks will weigh 15000*29.7
=445500 kg
= 445.5 tons
number of trips = 445.5/3 = 1485 trips

Question 699630: If you double the height and radius of a cylinder, why doesn't the surface area double? Thanks!
Found 2 solutions by lwsshak3, htmentor:
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If you double the height and radius of a cylinder, why doesn't the surface area double?
**
Because the surface area of the top and bottom varies as the square of the radius, that is, if you double the radius, the surface areas of the top and bottom increase 4 times. Area=πr^2

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Surface area of a cylinder

Doubling both the radius, r and the height, h gives

So the new surface area is four times the old surface area

Question 696306: If a circle of radius 6 were cut into 12 equal pieces, How much area would eah piece contain?
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If a circle of radius 6 were cut into 12 equal pieces, How much area would eah piece contain?
--------------

Divide by 12

Question 696308: How do you find the long leg of this special right triangle given the hypotenuse? (30,60,90)
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How do you find the long leg of this special right triangle given the hypotenuse? (30,60,90)
-----------------------
The short leg = 1/2 the hypotenuse.
You can use that and Pythagoras.
Or, the long leg = hyp*sine(60)

Question 696304: if a sphere's diameter doubles in size how much larger is the volume?
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if a sphere's diameter doubles in size how much larger is the volume?
------------

Volume is a function of the cube of the radius.
2x the radius --> 8x the volume.
---------
"How much larger" ---> 7 times larger, a 700% increase

Question 676228: what is the longest piece of dry spaghetti that will fit in a cylindrical can that has a radius of 3 inches and a height of 14 inches?
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14 inches. It can't be longer than the can's height, which is 14 inches. The can's radius doesn't matter to the length of the spaghetti.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

A solid steel has a 6 dm diameter and a height of 6 m.How many cubic dm of metal are in the cylinder?

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First you have to convert the height into dm
so, the height is 60dm
the volume of cylinder is = 3,14 . (1/2 . 6)^2 . 60 = 1695,6 cubic dm

Question 662353: The cube shown here has volume 1000 cm3. If its edges are all doubled in length its new volume will be
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The cube shown here has volume 1000 cm3. If its edges are all doubled in length its new volume will be
----
Original edge length = 1000^(1/3) = 10 cm
----
New edge length = 20
----
New volume = 20^3 = 8000 cm^3
=====================
Cheers,
Stan H.

Question 650764: a cylinder with radius 2 inches and height 4 inches has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder.
bobhilton34@yahoo.com

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a cylinder with radius 2 inches and height 4 inches has its radius tripled.
How many times greater is the volume of the larger cylinder than the smaller cylinder.
:
Since the radius is squared when you find the volume of a cylinder,
tripling the radius, increases the volume by 3^2 or 9 times
:
You can confirm this on your calc
enter:

and

Question 650148: I need help with a Precalculus problem:
The weight, W, of an object varies inversely as the square of the distance, d, from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find their weight when they are orbiting 400 mi above sea level.

Found 2 solutions by josmiceli, Alan3354:
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is called the constant of proportionality
given:
pounds
mi

---------------

The astronaut weighs about 200 pounds

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The weight, W, of an object varies inversely as the square of the distance, d, from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find their weight when they are orbiting 400 mi above sea level.
---------------
W = k/r^2
220 = k/3978^2
You can solve for k, but it's not necessary.

W = 181.64 pounds

Question 638170: P+2P=-15
Found 2 solutions by MathLover1, jim_thompson5910:
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Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

----------------------------------------------------------------------

So the solution is

Question 637320: summary of the chapter - representing solids on paper

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Question 637373: A right circular cylinder has height 6 and volume 54pie . What is the circumference of its base?
Found 2 solutions by Stitch, ewatrrr:
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The volume of a cylinder is: V = pi* r^2 * h
We are given V = 54pie
h = 6
54pi = pi * r^2 * 6
Divide both sides by 6
9pi = pi * r^2
Divide both sides by pi
9 = r^2
take the square root of both sides

3 = r
The circumference of a circle is 2*pi*r
So the circumference is: 2*pi*3 or

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Hi,

A right circular cylinder has height 6  and volume 54pie

r^2 = 9,  r = 3  and



Question 635727: the radius of a ball is 19 centimeters. what is its volume
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Hi,

the radius of a ball is 19 centimeters.
V =


Question 633881: What is the longest piece of straight dry spaghetti that will fit in a cylindrical can that has a radius of 3 inches and height of 10 inches?
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What is the longest piece of straight dry spaghetti that will fit in a cylindrical can that has a radius of 3 inches and height of 10 inches?
----
Right triangle with base = 6 inches and height = 10 inches.
---
hypotenuse = sqrt[6^2+10^2] = sqrt(136) = 11.66 inches
===========================
Cheers,
Stan H.
==============

Question 630064: Two cylindrical water tanks have the same dimensions. One is filled to a height of 4 ft while the other is filled to a height of 8 ft. What is the ratio of the amount of water in the two tanks?
Found 2 solutions by solver91311, Alan3354:
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2 times the height, everything else being equal, means 2 times the volume.

John

My calculator said it, I believe it, that settles it

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Two cylindrical water tanks have the same dimensions. One is filled to a height of 4 ft while the other is filled to a height of 8 ft. What is the ratio of the amount of water in the two tanks?
----------

h is 1st power --> linear function
Put another way, Vol = k*h, since pi*r^2 is the same for the 2 tanks.
4 to 8 --> 1 to 2 volume, the same ratio

Question 626129: Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 lb. what does the sphere weigh?
Thanks

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Two spheres of the same density have a ratio of 4 to 9 in surface area.
If the small sphere weighs 10 lb. what does the sphere weigh?
:
Surface area of the two spheres;
r1= radius of the small sphere
r2= radius of the larger sphere
=
cancel 4*pi
=
:
=
therefore
r1 = 2
r2 = 3
:
Vol is equiv of weight here
let w = weight of the larger sphere
=
Cancel and you have:
=
cross multiply
8w = 27*10
w =
w = 33.75, the weight of the larger sphere

Question 626141: a toy boat has a scale of 1:40 to an actual boat. If the mast on the toy boat weighs 216 Grams, how many metric tons does the actual boat's mast weigh?
I converted the 216 grams to 0.000216 ton and used the following equation:
1:40 = 0.000216:x to get an answer of .00864 metric tons.

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a toy boat has a scale of 1:40 to an actual boat. If the mast on the toy boat weighs 216 Grams, how many metric tons does the actual boat's mast weigh?
--------------
216*40 = 8640 grams
= 8.64 kg
= 0.00864 metric tons
=========================
The scale of models is based on linear measurements, not weights.
Model makers have no interest in the weights.

Question 621070: a cube of side 3cm contains a sphere withn it.if the sphere touches each face of the cube,find the volume of the space between the cube and the sphere.

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a cube of side 3cm contains a sphere within it.
if the sphere touches each face of the cube, find the volume of the space between the cube and the sphere.
Space = vol of the cube - vol of the sphere
S = -
S = 27 - 14.137
S = 12.863 cu/cm space

Question 619901: please help me solve this story problem. a silo is divided into three sections. The top section is one-fifth the length of the bottom section. The middles section is one-third the length of the bottom section. The total height of the silo is 460 ft. Find the length of the top section. Thank you in advance have been trying to formulate an equation for over an hour but am stuck.
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please help me solve this story problem. a silo is divided into three sections. The top section is one-fifth the length of the bottom section. The middles section is one-third the length of the bottom section. The total height of the silo is 460 ft. Find the length of the top section. Thank you in advance have been trying to formulate an equation for over an hour but am stuck.

Let the length of the bottom section be B
Then length of the top section = of B, or
Length of middle section = of B, or

Since total length of silo = 460 ft, then we have:

15B + 3B + 5B = 6,900 ------ Multiplying by LCD, 15

23B = 6,900

B, or length of bottom section = , or feet

Since length of bottom section = 300 ft, then length of top section = , or , or feet.

Question 619819: What is the volume of a cylinder
height = 7cm, using pi = 3.1?

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What is the volume of a cylinder
height = 7cm, using pi = 3.1?
--------------------

Question 619035: if a cylindrical jug is 20cm in height and has a capacity of one litre . . . what is its diameter??
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a litre is 1000 cm^3

pi * d^2 / 4 = 50 cm^2

Question 615254: a person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon
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person who weighs 200 pounds on earth would weigh about 32 pounds on the moon.
Find the weight of a person on earth who would weigh 15 pounds on the moon
:
Use a ratio equation to solve this:
Let w = his weight on the earth
:
=
Cross multiply
32w = 200 * 15
32w = 3000
w =
w = 93.75 lb on earth

Question 612818: A cylindrical container has base radius of 14cm and height 18cm.how many litres can it hold
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volume of cylinder=22/7*14*14*18=11088 cubic cm we have 1000cubic cm=1litre so volume of cylinder is 11.088 litre

Question 610699: find the volume of the largest cylinder with a circular base that can be inscribed in a cube which has a volume of 27m^3.

Found 2 solutions by jamesgunasekaran, lwsshak3:
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The volume of a cube with side s is . Hence find the side of the cube
which is going to be .
Hence a largest cylinder with base inscribed inside a cube will have the diameter 3 meters. and its maximum height will be the height of the cube. Hence in this case it is 3 meters. Hence the volume of a cylinder with the above parameters will be
Hence volume is = =

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find the volume of the largest cylinder with a circular base that can be inscribed in a cube which has a volume of 27m^3.
**
let x=length= width= height of cube
volume=x^3=27m^3
x=3 m
..
length of cylinder=3 m
Diameter of circular base=3 m
volume of cylinder=πr^2*3=π(3/2)^2*3=27π/4
ans:
largest cylinder with a circular base that can be inscribed in the cube=27π/4 m^3

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