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ISEE Upper Level Quantitative : How to find the volume of a cylinder

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Example Questions

Example Question #1 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a radius of 6 meters and a height of 11 meters? Use 3.14 for $\pi$ .

Note: The formula for the volume of a cylinder is:

$V=\pi r^2h$

Possible Answers:

114.44m^3

207.24m^3

396m^3

1243.44 m^3

1432.23m^3

Correct answer:

1243.44 m^3

Explanation:

To calculate the volume, you must plug into the formula given in the problem. When you plug in, it should look like this: V=(3.14)(6^2)(11) . Multiply all of these out and you get 1243.44m^3 . The units are cubed because volume is always cubed.

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Example Question #1 : How To Find The Volume Of A Cylinder

The volume of a cylinder whose height is twice the diameter of its base is one cubic yard. Give its radius in inches.

Possible Answers:

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {4 \pi } \textrm{ in}$

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {2 \pi } \textrm{ in}$

$\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi } \textrm{ in}$

$\frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

Correct answer:

$\frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

Explanation:

The volume of a cylinder with base radius and height is

$V = \pi r^{2}h$

The diameter of this circle is ; its height is twice this, or . Therefore, the formula becomes

$V = \pi r^{2} \cdot 4r = 4\pi r^{3}$

Set this volume equal to one and solve for :

$4\pi r^{3} = 1$

$4\pi r^{3} \div 4\pi = 1 \div 4\pi$

$r ^{3}= \frac{1}{4\pi }$

$r =\sqrt[3]{ \frac{1}{4\pi }} =\frac{ \sqrt[3]{ 1 }} { \sqrt[3]{ 4\pi }} =\frac{ \sqrt[3]{ 1 } \cdot \sqrt[3]{ 2 \pi^{2} } } { \sqrt[3]{ 4\pi } \cdot \sqrt[3]{ 2 \pi^{2} }}=\frac{ \sqrt[3]{ 2 \pi^{2} } } {\sqrt[3]{ 8\pi^{3} }}=\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi }$

This is the radius in yards; multiply by 36 to get the radius in inches.

$\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi } \cdot 36 = \frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi }$

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Example Question #3 : How To Find The Volume Of A Cylinder

What is the height of a cylinder with a volume of $646.875\pi$ in^3 and a radius of 7.5 ?

Possible Answers:

28125.5

11.5

86.25

56250

22.5

Correct answer:

11.5

Explanation:

Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$646.875\pi = \pi * 7.5^2 * h= \pi * 56.25 * h$

Solve for :

h = 11.5

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Example Question #4 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a height of in. and a radius of in?

Possible Answers:

$204\pi$ in^3

$300\pi$ in^3

$180\pi$ in^3

$720\pi$ in^3

$408\pi$ in^3

Correct answer:

$720\pi$ in^3

Explanation:

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$A = \pi * 12^2 * 5=720\pi$

This is the volume of the cylinder.

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Example Question #5 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a height of in. and a radius of 2.5 in?

Possible Answers:

$87.5\pi$ in^3

$82.5\pi$ in^3

$42.25\pi$ in^3

$70\pi$ in^3

$35\pi$ in^3

Correct answer:

$87.5\pi$ in^3

Explanation:

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$A = \pi * 2.5^2 * 14=87.5\pi$

This is the volume of the cylinder.

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Example Question #51 : Solid Geometry

What is the radius of a cylinder with a volume of $562.5\pi$ in^3 and a height of ?

Possible Answers:

$15\pi$

7.5

56.25

$56.25\pi$

Correct answer:

7.5

Explanation:

Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$562.5\pi = \pi * r^2 * 10$

Solve for :

56.25=r^2

Using a calculator to calculate $\sqrt{56.25}$ , you will see that r = 7.5

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ISEE Upper Level Quantitative : How to find the volume of a cylinder

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #1 : How To Find The Volume Of A Cylinder

Example Question #3 : How To Find The Volume Of A Cylinder

Example Question #4 : How To Find The Volume Of A Cylinder

Example Question #5 : How To Find The Volume Of A Cylinder

Example Question #51 : Solid Geometry

All ISEE Upper Level Quantitative Resources

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