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ISEE Upper Level Quantitative : Cylinders

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Example Question #341 :Geometry

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:

396m^3

1432.23m^3

114.44m^3

1243.44 m^3

207.24m^3

有限公司rrect 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 #342 :Geometry

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:

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

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

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

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

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

有限公司rrect answer:

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

Explanation:

The volume of a cylinder with base radiusand heightis

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

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 #343 :Geometry

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

Possible Answers:

11.5

86.25

56250

28125.5

22.5

有限公司rrect 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 #51 :Solid Geometry

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

Possible Answers:

$720\pi$ in^3

$408\pi$ in^3

$300\pi$ in^3

$180\pi$ in^3

$204\pi$ in^3

有限公司rrect 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 #351 :Geometry

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

Possible Answers:

$70\pi$ in^3

$87.5\pi$ in^3

$42.25\pi$ in^3

$82.5\pi$ in^3

$35\pi$ in^3

有限公司rrect 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 #352 :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

$56.25\pi$

56.25

有限公司rrect 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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Example Question #353 :Geometry

What is the surface area of a cylinder of heightin., with a radius ofin?

Possible Answers:

$152\pi$ in^2

$240\pi$ in^2

$120\pi$ in^2

$136\pi$ in^2

$122\pi$ in^2

有限公司rrect answer:

$152\pi$ in^2

Explanation:

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 4^2 = \pi * 16$

You need to double this for thetwobases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Example Question #354 :Geometry

What is the surface area of a cylinder having a base of radiusin and a height ofin?

Possible Answers:

$308\pi$ in^2

$363\pi$ in^2

$33\pi$ in^2

$99\pi$ in^2

$212\pi$ in^2

有限公司rrect answer:

$308\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 11^2 = \pi * 121$

You need to double this for thetwobases:

$2 * 121 * \pi = 242 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 11* 3 = 66 * \pi$

Therefore, the total surface area is:

$242 * \pi + 66 * \pi = 308\pi$

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Example Question #355 :Geometry

What is the surface area of a cylinder with a height ofin. and a diameter ofin?

Possible Answers:

$28\pi$ in^2

$36\pi$ in^2

$14\pi$ in^2

$22\pi$ in^2

$57\pi$ in^2

有限公司rrect answer:

$36\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 2^2 = \pi * 4$

You need to double this for thetwobases:

$2 * 4 * \pi = 8 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 2 * 7 = 28 * \pi$

Therefore, the total surface area is:

$28\pi + 8\pi = 36\pi$

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Example Question #1 :Cylinders

The volume of a cylinder with height ofis $275\pi$ in^3 . What is its surface area?

Possible Answers:

$160\pi$ in^2

$82\pi$ in^2

$135\pi$ in^2

$66\pi$ in^2

$55\pi$ in^2

有限公司rrect answer:

$160\pi$ in^2

Explanation:

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

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

For our values this is:

$275\pi = \pi * r^2 * 11$

Solving for, we get:

r^2 = 25

Hence, r = 5

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 5^2 = \pi * 25$

You need to double this for thetwobases:

$2 * 25 * \pi = 50 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 5 * 11 = 110 * \pi$

Therefore, the total surface area is:

$50\pi + 110\pi = 160\pi$

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ISEE Upper Level Quantitative : Cylinders

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #341 :Geometry

Example Question #342 :Geometry

Example Question #343 :Geometry

Example Question #51 :Solid Geometry

Example Question #351 :Geometry

Example Question #352 :Geometry

Example Question #353 :Geometry

Example Question #354 :Geometry

Example Question #355 :Geometry

Example Question #1 :Cylinders

All ISEE Upper Level Quantitative Resources

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