Unit 8 · Test

Unit 8 test: Volume

15 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This test covers the volume of cylinders, cones and spheres, including hemispheres, slant height, missing dimensions and combined solids. Type pi for $\pi$ when an answer is in terms of $\pi$ .

Question 1

A cylinder has a radius of 5 cm and a height of 3 cm. Find its volume in cubic centimeters, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

A candle shaped like a cylinder is 4 inches across and 9 inches tall. Find its volume in cubic inches, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 3

A cylindrical tank has a radius of 10 ft and a height of 2 ft. Use $3.14$ for $\pi$ to find its volume in cubic feet. Round to the nearest whole number.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

A cylinder has a volume of $180\pi$ cubic meters and a radius of 6 m. What is its height, in meters?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

A cone has a radius of 4 cm and a height of 9 cm. Find its volume in cubic centimeters, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

Find the volume of this cone in cubic inches, in terms of $\pi$ .

The radius is 3 in and the height is 7 in.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

A cylinder has a volume of $81\pi$ cubic cm. A cone has the same base and the same height. What is the cone's volume?

Question 8

A cone has a radius of 8 m and a slant height of 17 m. Find its volume in cubic meters, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

A cone has a volume of $32\pi$ cubic feet and a radius of 4 ft. What is its height, in feet?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

Find the volume of a sphere with a radius of 6 cm, in cubic centimeters, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

A bowl is a hemisphere with a diameter of 6 inches. How much can it hold, in cubic inches? Give your answer in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

A sphere has a volume of $972\pi$ cubic meters. What is its radius, in meters?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

The radius of a sphere is doubled. How does its volume change?

Question 14

A toy is a cone with a hemisphere on top. The cone has a radius of 6 cm and a height of 10 cm, and the hemisphere has the same radius. Find the total volume in cubic centimeters, in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

A ball with a radius of 6 in is packed in a cylindrical box that fits it snugly: the box has a radius of 6 in and a height of 12 in. How much empty space is in the box, in cubic inches? Give your answer in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.