How to find the volume of a cylinder - GRE Quantitative Reasoning

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Question

A cylinder has a height of 4 and a circumference of 16π. What is its volume

Answer

circumference = πd

d = 2r

volume of cylinder = πr2h

r = 8, h = 4

volume = 256π

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Question

Rusty is considering making a cylindrical grain silo to store his crops. He has an area that is 6 feet long, 6 feet wide and 12 feet tall to build a cylinder in. What is the maximum volume of grain that he can store in this cylinder?

Answer

The maximum cylindrical base can have a diameter of 6 and therefore a radius of 3. The formula for the volume of a cylinder is $\dpi{100} \small \pi r^{2}h$ , which in this case is $\dpi{100} \small 3\times 3\times 12\times \pi$ .

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Question

A cylinder with volume of $192\pi:in^3$ and a radius of has its radius doubled. What is the volume of the new cylinder?

Answer

To begin, you must solve for the height of the original cylinder. We know:

$V=\pi r^2h$

For our values, we know:

$192\pi=\pi 4^2h=16\pi h$

Now, divide both sides by $16\pi$ :

So, if we have a new radius of , our volume will be:

$V=8^212\pi=768\pi:in^3$

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