Cylinders

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ISEE Upper Level Quantitative Reasoning › Cylinders

Questions 1 - 10

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?

$2250 \pi ft^3$

$22.50 \pi ft^3$

$4500 \pi ft^3$

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

$2250 \pi ft^3$

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?

$2250 \pi ft^3$

$22.50 \pi ft^3$

$4500 \pi ft^3$

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

$2250 \pi ft^3$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$160 \pi$

$84\pi$

$48\pi$

$40\pi$

$80\pi$

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: $160 \pi$

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

$160 \pi$

$84\pi$

$48\pi$

$40\pi$

$80\pi$

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: $160 \pi$

The axle for a toy car has a length of 4 inches and a diameter of a quarter inch. What is the volume of the axle? Assume it is a cylinder.

$\frac{\pi}{16}in^3$

$\frac{\pi}{2}in^3$

$\frac{\pi}{4}in^3$

$16\pi in^3$

Explanation

The axle for a toy car has a length of 4 inches and a diameter of a quarter inch. What is the volume of the axle? Assume it is a cylinder.

Use the following formula for volume of a cylinder

$V_{cylinder}=\pi r^2h$

Where r and h are our radius and height, respectively.

In this case, we first need to change our diameter to radius. Because our diameter is one quarter of an inch, our radius will be one eighth of an inch.

Plug it in to get:

$V_{cylinder}=\pi (\frac{1}{8})^2*4=\pi*\frac{1}{64}in^2*4in=\frac{4\pi}{64}in^3$

Simplify to get:

$\frac{4\pi}{64}in^3=\frac{\pi}{16}in^3$

The axle for a toy car has a length of 4 inches and a diameter of a quarter inch. What is the volume of the axle? Assume it is a cylinder.

$\frac{\pi}{16}in^3$

$\frac{\pi}{2}in^3$

$\frac{\pi}{4}in^3$

$16\pi in^3$

Explanation

The axle for a toy car has a length of 4 inches and a diameter of a quarter inch. What is the volume of the axle? Assume it is a cylinder.

Use the following formula for volume of a cylinder

$V_{cylinder}=\pi r^2h$

Where r and h are our radius and height, respectively.

In this case, we first need to change our diameter to radius. Because our diameter is one quarter of an inch, our radius will be one eighth of an inch.

Plug it in to get:

$V_{cylinder}=\pi (\frac{1}{8})^2*4=\pi*\frac{1}{64}in^2*4in=\frac{4\pi}{64}in^3$

Simplify to get:

$\frac{4\pi}{64}in^3=\frac{\pi}{16}in^3$

Find the volume of a cylinder with the following measurements: