Worksheet Grade 8 Math

Dunmarsh Booster Station: Volume of a Cylindrical and Spherical Tank

A grade 8 worksheet where students find the volume of a fictional pump station's cylindrical storage tank and spherical pressure tank in cubic feet and gallons.

Grade: Grade 8
Subject: Math
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

8.G.C.9 Common Core Math

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

How this material aligns: Students apply the cylinder volume formula in item 2 and the sphere volume formula in item 5 for the two tank shapes at the pump station, then convert each volume to gallons in items 3 and 6, the real-world volume work this standard requires.

All materials for 8.G.C.9 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate the volume of a cylinder and a sphere in cubic feet.
Students will convert a tank volume from cubic feet to gallons.

Vocabulary

Key words: volume, cylinder, sphere, radius

Teacher overview

The Dunmarsh booster station is a fictional pumping station that keeps water pressure steady for a hilly neighborhood. It uses two tanks with different shapes: a tall cylindrical storage tank and a spherical pressure tank. This worksheet has students find each tank's volume and convert it to gallons. A common mistake is using the tank's diameter in place of its radius, so students should find the radius first in items 1 and 4 before using either volume formula.

Dunmarsh Booster Station: Volume of a Cylindrical and Spherical Tank — Grade 8 Math

Name: ____________________________ Date: ______________

Student Worksheet

Use these values from the fictional Dunmarsh booster station. Use 3.14 for pi, and use 7.48 gallons per cubic foot.

The cylindrical storage tank is 20 feet across and 30 feet tall.
The spherical pressure tank is 12 feet across.

Cylinder volume = 3.14 x radius x radius x height. Sphere volume = (4 divided by 3) x 3.14 x radius x radius x radius.

Find the radius of the cylindrical storage tank.
Find the volume of the cylindrical storage tank in cubic feet. Show your work.
Convert your answer from item 2 to gallons by multiplying by 7.48. Round to the nearest gallon.
Find the radius of the spherical pressure tank.
Find the volume of the spherical pressure tank in cubic feet. Show your work.
Convert your answer from item 5 to gallons by multiplying by 7.48. Round to the nearest gallon.
Using cubic feet, how many times as much water does the cylindrical tank hold as the spherical tank? Round to the nearest tenth.
During the day the station keeps the cylindrical tank 80 percent full. How many gallons is that? Use your answer from item 3.
Explain your reasoning: A worker guesses that doubling the sphere's diameter would double its volume. Use the sphere volume formula to explain why that guess is wrong.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 10 feet.
The radius is half the diameter: 20 / 2 = 10 feet.
Answer: 9,420 cubic feet.
Volume = 3.14 x 10 x 10 x 30 = 3.14 x 100 x 30 = 9,420 cubic feet.
Answer: 70,462 gallons.
9,420 x 7.48 = 70,461.6, which rounds to 70,462 gallons.
Answer: 6 feet.
The radius is half the diameter: 12 / 2 = 6 feet.
Answer: 904.32 cubic feet.
Volume = (4 / 3) x 3.14 x 6 x 6 x 6 = (4 / 3) x 3.14 x 216. First 3.14 x 216 = 678.24, then 678.24 x 4 = 2,712.96, then divided by 3 = 904.32 cubic feet.
Answer: 6,764 gallons.
904.32 x 7.48 = 6,764.3, which rounds to 6,764 gallons.
Answer: 10.4 times.
9,420 / 904.32 = 10.416, which rounds to 10.4 times as much.
Answer: 56,370 gallons.
70,462 x 0.80 = 56,369.6, which rounds to 56,370 gallons.
Answer: Volume depends on the radius cubed, not just the radius, so doubling the diameter doubles the radius and multiplies the volume by 2 x 2 x 2, which is 8. Doubling the diameter makes the volume 8 times as large, not 2 times.

Differentiation

Support

Provide a formula card with both volume formulas and the cubic-foot-to-gallon conversion, and pre-solve the radii (10 feet and 6 feet) so students can focus on the volume steps. Allow a calculator for every computation item.

Extension

Ask students to find the diameter a spherical tank would need to hold the same volume as the cylindrical storage tank, working backward from the cylinder's cubic-foot volume and the sphere volume formula.

ELL supports

Provide a labeled diagram of both tanks that marks diameter and radius as separate lengths, and give a sentence frame for item 9: "Doubling the diameter multiplies the volume by ___ because the formula uses the radius ___ times."