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SAT Math : Geometry

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Example Questions

Example Question #21 : Cylinders

Two cylinders are full of milk. The first cylinder is 9” tall and has a base diameter of 3”. The second cylinder is 9” tall and has a base diameter of 4”. If you are going to pour both cylinders of milk into a single cylinder with a base diameter of 6”, how tall must that cylinder be for the milk to fill it to the top?

Possible Answers:

12"

6.25"

30"

Correct answer:

6.25"

Explanation:

Volume of cylinder = π * (base radius)² x height = π * (base diameter / 2 )² x height

Volume Cylinder 1 = π * (3 / 2 )² x 9 = π * (1.5 )² x 9 = π * 20.25

Volume Cylinder 2 = π * (4 / 2 )² x 9 = π * (2 )² x 9 = π * 36

Total Volume = π * 20.25 + π * 36

Volume of Cylinder 3 = π * (6 / 2 )² x H = π * (3 )² x H = π * 9 x H

Set Total Volume equal to the Volume of Cylinder 3 and solve for H

π * 20.25 + π * 36 = π * 9 x H

20.25 + 36 = 9 x H

H = (20.25 + 36) / 9 = 6.25”

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Example Question #842 : Geometry

Determine the volume of a cylinder if the diameter of the base is 2 and the cylinder height is 10.

Possible Answers:

$5\pi$

$40\pi$

$\frac{5}{2}\pi$

$20\pi$

$10\pi$

Correct answer:

$10\pi$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2 h$

The base of a cylinder is a circle, and the radius is half the diameter given.

$r=\frac{d}{2}=\frac{2}{2}=1$

Substitute the radius and the given height to the volume equation.

$V=\pi (1)^2 (10)= 10\pi$

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Example Question #21 : How To Find The Volume Of A Cylinder

The radius of the base of the cylinder is $\frac{2}{3}$ . The height of the cylinder is $\frac{1}{5}$ . What is the volume?

Possible Answers:

$\frac{4}{15}\pi$

$\frac{4}{45}\pi$

$\frac{11}{15}\pi$

$\frac{2}{7}\pi$

$\frac{4}{225}\pi$

Correct answer:

$\frac{4}{45}\pi$

Explanation:

Write the volume formula of the cylinder and substitute the values.

$V=\pi r^2 h = \pi(\frac{2}{3})^2(\frac{1}{5}) = \pi (\frac{4}{9})(\frac{1}{5})= \frac{4}{45}\pi$

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Example Question #844 : Geometry

What is the volume of a cylinder with a radius of 6 and a height of 8?

Possible Answers:

$72\pi$

$144\pi$

$288 \pi$

$96\pi$

$576\pi$

Correct answer:

$288 \pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2 h$

Subsstitute the given radius and height into the formula.

$V=\pi (6)^2 (8) = \pi \cdot 36 \cdot 8$

$V=288 \pi$

The volume is $288 \pi$ .

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Example Question #841 : Sat Mathematics

Find the volume aof a cylinder whose heigh is 5 and radius is 3.

Possible Answers:

$75\pi$

$14\pi$

$28\pi$

$45\pi$

Correct answer:

$45\pi$

Explanation:

To solve, simply use the formula for the volume of a cylinder Thus,

$V=\pi{r^2}h=\pi*3^2*5=45\pi$

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Example Question #846 : Geometry

Find the volume of a cylinder with radius 4 and height 5.

Possible Answers:

$9\pi$

$80\pi$

$20\pi$

$100\pi$

Correct answer:

$80\pi$

Explanation:

To solve, simply use the formula for the volume of a cylinder.

$V=\pi{r^2}h=\pi*{4^2}*5=\pi*16*5=80\pi$

If you don't have the formula memorized, remember that a cylinder is made from a circular base, just with a third dimension of height. So, simply just take the formula for the area of a circle and multiply is by the height.

$A=\pi{r^2}$

h=height

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

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Example Question #21 : How To Find The Volume Of A Cylinder

Find the volume of a cone with radius 2 and height 4.

Possible Answers:

$\frac{32\pi}{3}$

$60\pi$

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

$30\pi$

Correct answer:

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

Explanation:

To solve, simply use the formula for the volume of a cone. Thus,

$V=\frac{1}{3}\pi{r^2}h=\frac{1}{3}\pi*{2^2}*4=\frac{1}{3}\pi*4*4=\frac{16\pi}{3}$

To remember the formula for volume of a cone, it helps to break it up into it's base and height. The base is a circle and the height is just h. Now, just multiplying those two together would give you the formula of a cylinder (see problem 3 in this set). So, our formula is going to have to be just a portion of that. Similarly to volume of a pyramid, that fraction is one third.

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Example Question #22 : Cylinders

The volume of a right cylinder is $16\pi.$ It's radius is one-half of its height. What is the height of the cylinder?

Possible Answers:

$6\sqrt\pi$

$4\sqrt\pi$

Correct answer:

Explanation:

If the radius is one-half of the height of the cylinder, we can say that

$r=\frac{1}{2}h$

Then, we can substitute this expression into our equation for the volume of a right cylinder.

$V=\pi r^2h$

$16\pi=\pi (\frac{1}{2}h)^2h$

Now, we can simplify and solve for h.

$16\pi=\pi (\frac{1}{4}h^2)h$

$16\pi=\pi \cdot \frac{1}{4}h^3$

$16=\frac{1}{4}h^3$

64=h^3

$h=\sqrt[3]{64}=4$

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Example Question #22 : How To Find The Volume Of A Cylinder

Which of the following will quadruple a cylinder's volume?

Doubling the radius
Quadripling the radius
Quadrupling the height

Possible Answers:

1 and 3

3 only

2 only

1 and 2

1 only

Correct answer:

1 and 3

Explanation:

Remember our volume equation: $V_{cyl} = \pi r^2 h$

This means that the volume of a cylinder varies directly by the square of its radius and directly by its height. That means you need to quadruple the height to quadruple the volume but also that you only have to double the radius to quadruple the volume because

$\pi (2r)^2 h = \pi(4r^2)h = 4\pi r^2 h = 4V_{cyl}$

where $V_{cyl}$ is the original cylinder volume.

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Example Question #23 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with height of 10cm and diameter of 4cm?

Possible Answers:

$4\pi cm^3$

$80\pi cm^3$

$20\pi$

$10\pi cm^3$

$40\pi cm^3$

Correct answer:

$40\pi cm^3$

Explanation:

$Volume=\pi r^2h$

The height is given: 10cm

The diameter is 4cm so the radius is half of that: 2cm

$Volume=\pi 2^2*10$

$Volume=40\pi cm^3$

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SAT Math : Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Cylinders

Example Question #842 : Geometry

Example Question #21 : How To Find The Volume Of A Cylinder

Example Question #844 : Geometry

Example Question #841 : Sat Mathematics

Example Question #846 : Geometry

Example Question #21 : How To Find The Volume Of A Cylinder

Example Question #22 : Cylinders

Example Question #22 : How To Find The Volume Of A Cylinder

Example Question #23 : How To Find The Volume Of A Cylinder

All SAT Math Resources

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