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ISEE Upper Level Math : Solid Geometry

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

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6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Find the volume of a cylinder with the following measurements:

diameter = 8cm
height = 5cm

Possible Answers:

$80\pi \text{ cm}^3$

$60\pi \text{ cm}^3$

$20\pi \text{ cm}^3$

$40\pi \text{ cm}^3$

$100\pi \text{ cm}^3$

Correct answer:

$80\pi \text{ cm}^3$

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 8cm. We know that the diameter is two times the radius. Therefore, the radius is 4cm.

We also know the height of the cylinder is 5cm.

Knowing this, we can substitute into the formula.

$V = \pi \cdot (4\text{cm})^2 \cdot 5\text{cm}$

$V = \pi \cdot 16\text{cm}^2 \cdot 5\text{cm}$

$V = \pi \cdot 80\text{cm}^3$

$V = 80\pi \text{ cm}^3$

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Example Question #1 : Cylinders

Find the volume of a cylinder with a diameter of 8in and a height of 7in.

Possible Answers:

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

$121\pi \text{ in}^3$

$78\pi \text{ in}^3$

$68\pi \text{ in}^3$

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

Correct answer:

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

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 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We also know the height of the cylinder is 7in.

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

$V = \pi \cdot(4\text{in})^2 \cdot 7\text{in}$

$V = \pi \cdot 16\text{in}^2 \cdot 7\text{in}$

$V = \pi \cdot 112\text{in}^3$

$V = 112\pi \text{ in}^3$

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Example Question #2 : Cylinders

Find the volume of a cylinder with a diameter of 14in and a height of 12in.

Possible Answers:

$273\pi \text{ in}^3$

$168\pi \text{ in}^3$

$588\pi \text{ in}^3$

$456\pi \text{ in}^3$

$336\pi \text{ in}^3$

Correct answer:

$588\pi \text{ in}^3$

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 14in. We also know the diameter is two times the radius. Therefore, the radius is 7in.

We know the height of the cylinder is 12in.

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

$V = \pi \cdot (7\text{in})^2 \cdot 12\text{in}$

$V = \pi \cdot 49\text{in}^2 \cdot 12\text{in}$

$V = \pi \cdot 588\text{in}^3$

$V = 588\pi \text{ in}^3$

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Example Question #3 : Cylinders

Your family owns a farm with a silo for storing grain. If the silo is 40 feet tall and 15 feet in diameter, what volume of grain can it hold?

Possible Answers:

$22.50 \pi ft^3$

$2250 \pi ft^3$

$4500 \pi ft^3$

2250 ft^2

Correct answer:

$2250 \pi ft^3$

Explanation:

Your family owns a farm with a silo for storing grain. If the silo is 40 feet tall and 15 feet in diameter, what volume of grain can it hold?

Begin with the formula for volume of a cylinder.

$V=\pi r^2h$

A cylinder is just a circle with height.

So, we know the height is 40 ft, but what is r?

If you said 15, you would be on track to get the problem wrong. That is because the diameter is 15 ft, so our radius is only 7.5 ft.

Plug these in to get our answer:

$V=\pi (7.5ft)^2(40ft)=2250 \pi ft^3$

Our answer should be

$2250 \pi ft^3$

Report an Error

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

Let $\pi = 3.14$

Find the volume of a cylinder with a diameter of 12cm and a height of 7cm.

Possible Answers:

$263.76\text{cm}^3$

$923.16\text{cm}^3$

$527.52\text{cm}^3$

$131.88\text{cm}^3$

$791.28\text{cm}^3$

Correct answer:

$791.28\text{cm}^3$

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 is 12cm. We know that the diameter is two times the radius. Therefore, the radius is 6cm.

We know the height of the cylinder is 7cm.

We know that $\pi = 3.14$ .

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

$V = 3.14 \cdot (6\text{cm})^2 \cdot 7\text{cm}$

$V = 3.14 \cdot 36\text{cm}^2 \cdot 7\text{cm}$

$V = 3.14 \cdot 252\text{cm}^3$

$V = 791.28\text{cm}^3$

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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:

$V=257.25 \pi cm^3$

Report an Error

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

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

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

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

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

Report an Error

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

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

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

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

Report an Error

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

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

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

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

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

Report an Error

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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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Solid Geometry

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

All ISEE Upper Level Math Resources

Example Questions

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

Example Question #1 : Cylinders

Example Question #2 : Cylinders

Example Question #3 : Cylinders

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

Example Question #431 : Geometry

Example Question #111 : Solid Geometry

Example Question #112 : Solid Geometry

Example Question #113 : Solid Geometry

Example Question #111 : Solid Geometry

All ISEE Upper Level Math Resources

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