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ISEE Upper Level Math : Geometry

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Example Questions

Example Question #431 : Geometry

You have a tennis ball canister which is cylindrical. If the radius of the cylinder is 3.5 cm, and the height is 21 cm, what is the volume of the canister?

Possible Answers:

$V=73.5 \pi cm^3$

$V=257.25 \pi cm^3$

$V=25.725 \pi cm^3$

V=257.25 cm^3

Correct answer:

$V=257.25 \pi cm^3$

Explanation:

You have a tennis ball canister which is cylindrical. If the radius of the cylinder is 3.5 cm, and the height is 21 cm, what is the volume of the canister?

Begin with the formula for volume of a cylinder:

$V=\pi r^2 h$

Where r is our radius and h is our height.

Note that the formula is just the formula for the area of a circle times the height, because a cylinder is really just a circle with height.

Now, plug in what we know and solve for V

$V=\pi (3.5cm)^2 (21cm)=\pi(12.25cm*21cm)=257.25 \pi cm^3$

So our answer is:

$V=257.25 \pi cm^3$

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Example Question #111 : Solid Geometry

A cylinder has the following measurements:

Height: 6in
Diameter: 16in

Find the volume.

Possible Answers:

$96\pi \text{ in}^3$

$48\pi \text{ in}^3$

$384\pi \text{ in}^3$

$288\pi \text{ in}^3$

$576\pi \text{ in}^3$

Correct answer:

$384\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 16in. We also know the diameter is two times the radius. Therefore, the radius is 8in.

We also know the height of the cylinder is 6in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot(8\text{in})^2 \cdot 6\text{in}$

$V = \pi \cdot 64\text{in}^2 \cdot 6\text{in}$

$V = \pi \cdot 384\text{in}^3$

$V = 384\pi \text{ in}^3$

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Example Question #112 : Solid Geometry

A cylinder has the following measurements:

Height: 12in
Diameter: 10in

Find the volume.

Possible Answers:

$300\pi \text{ in}^3$

$720\pi \text{ in}^3$

$360\pi \text{ in}^3$

$576\pi \text{ in}^3$

$120\pi \text{ in}^3$

Correct answer:

$300\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

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

where r is the radius, and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 10in. We also know the diameter is two times the radius. Therefore, the radius is 5in.

We know the height of the cylinder is 12in.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (5\text{in})^2 \cdot 12\text{in}$

$V = \pi \cdot 25\text{in}^2 \cdot 12\text{in}$

$V = \pi \cdot 300\text{in}^3$

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Example Question #113 : Solid Geometry

Find the volume of a cylinder with a height of 9in and a radius of 8in.

Possible Answers:

$324\pi \text{ in}^3$

$648\pi \text{ in}^3$

$144\pi \text{ in}^3$

$576\pi \text{ in}^3$

$212\pi \text{ in}^3$

Correct answer:

$576\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the radius of the cylinder is 8in and the height of the cylinder is 9in.

So, we get

$V = \pi \cdot (8\text{in})^2 \cdot 9\text{in}$

$V = \pi \cdot 64\text{in}^2 \cdot 9\text{in}$

$V = \pi \cdot 576\text{in}^3$

$V = 576\pi \text{ in}^3$

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Example Question #111 : Solid Geometry

For a cylinder, if the radius of the base is 4, and the height is 10, what is the volume?

Possible Answers:

$84\pi$

$48\pi$

$80\pi$

$160 \pi$

$40\pi$

Correct answer:

$160 \pi$

Explanation:

Write the formula to find the volume of a cylinder.

$V = \pi r^2h$

Substitute the known dimensions.

$V = \pi (4^2)(10)$

Solve for the volume.

$V =160 \pi$

The answer is: $160 \pi$

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

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Possible Answers:

$144 \pi mm^2$

432 mm

$432 \pi mm^2$

$288 \pi mm^2$

Correct answer:

$432 \pi mm^2$

Explanation:

If a cylinder has a height of 6 mm and a radius of 12 mm, what is its surface area?

Find surface area with the following formula:

$A=2\pi r h +2\pi r^2$

This works because we are adding the area of the two bases to the area of the side.

Plug in and simplify:

$A=2\pi (12mm)(6mm) +2\pi (12mm)^2=144\pi mm^2+288\pi mm^2=432 \pi mm^2$

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Example Question #433 : Geometry

Find the volume of a cylinder with a diameter of 14cm and a height of 8cm.

Possible Answers:

$896\pi \text{ cm}^3$

$112\pi \text{ cm}^3$

$56\pi \text{ cm}^3$

$976\pi \text{ cm}^3$

$392\pi \text{ cm}^3$

Correct answer:

$392\pi \text{ cm}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the diameter of the cylinder is 14cm. We also know that the diameter is two times the radius. Therefore, the radius is 7cm.

We know the height of the cylinder is 8cm.

Knowing all of this, we can substitute into the formula. We get

$V = \pi \cdot (7\text{cm})^2 \cdot 8\text{cm}$

$V = \pi \cdot 49\text{cm}^2 \cdot 8\text{cm}$

$V = \pi \cdot 392\text{cm}^3$

$V = 392\pi \text{ cm}^3$

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ISEE Upper Level Math : Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #431 : Geometry

Example Question #111 : Solid Geometry

Example Question #112 : Solid Geometry

Example Question #113 : Solid Geometry

Example Question #111 : Solid Geometry

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

Example Question #433 : Geometry

All ISEE Upper Level Math Resources

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