Worksheet Grade 8 Art & Music

Confluence Plaza Fountain: A Water-Sculpture Volume Worksheet

A grade 8 art-design worksheet where students size a public fountain's cylinder, cone, and sphere forms with volume formulas and a cubic-foot-to-gallon conversion.

Grade: Grade 8
Subject: Art & Music
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: None

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, cone, and sphere volume formulas to size the sculptural forms of a public fountain, the real-world volume problems this standard names, and convert cubic feet to gallons.

All materials for 8.G.C.9 →

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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 cylinder, cone, and sphere forms using the standard volume formulas.
Students will convert a volume in cubic feet to gallons using a standard conversion.
Students will explain how changing a form's radius by a given factor affects its volume more than changing its depth by the same factor.

Vocabulary

Key words: cylinder, cone, sphere, radius, volume

Teacher overview

Confluence Plaza is a fictional town square in the town of Halden, and its centerpiece is a sculpted fountain built from a few simple forms: a wide cylinder catch basin at the bottom, a smaller cylinder spillway bowl above it, a cone-shaped stone spire, and a stone sphere resting on top. An artist who designs a fountain has to know how much water each part holds and how much stone each solid form uses, and both come down to volume. This worksheet has students size the fountain's forms using the volume formulas for cylinders, cones, and spheres, then convert one water volume into gallons. Use the value pi is about 3.14 and the conversion that 1 cubic foot equals 7.48 gallons.

Confluence Plaza Fountain: A Water-Sculpture Volume Worksheet — Grade 8 Art & Music

Name: ____________________________ Date: ______________

Student Worksheet

Use these formulas and round as each item asks:

Cylinder volume equals pi times radius squared times height.
Cone volume equals one-third times pi times radius squared times height.
Sphere volume equals four-thirds times pi times radius cubed.
Use pi is about 3.14, and 1 cubic foot equals 7.48 gallons.

The lower catch basin is a cylinder with a radius of 6 feet. The water in it is 1.5 feet deep. Find the volume of water in cubic feet.
Convert the basin's water volume from item 1 into gallons. Round to the nearest gallon.
The upper spillway bowl is a cylinder with a radius of 3 feet and a water depth of 1 foot. Find its water volume in cubic feet.
Convert the bowl's water volume from item 3 into gallons. Round to the nearest gallon.
Add your cubic-foot answers from items 1 and 3 to find the total water volume held by the basin and the bowl together.
The stone spire is a cone with a radius of 2 feet and a height of 6 feet. Find its volume in cubic feet.
The stone ball on top is a sphere with a radius of 1.5 feet. Find its volume in cubic feet. Round to the nearest hundredth.
The artist wants the basin to hold about 500 more gallons of water. How many more cubic feet of water is that? Round to the nearest whole cubic foot.
The basin's radius stays 6 feet. How much deeper must the water be to add the extra cubic feet from item 8? Round to the nearest tenth of a foot.
Explain your reasoning: to add water capacity, the artist could double the basin's radius or double its water depth. Which change adds more volume, and why?

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: 169.56 cubic feet. Cylinder volume is 3.14 times 6 squared times 1.5, which is 3.14 times 36 times 1.5 equals 169.56.
Answer: 1,268 gallons. 169.56 times 7.48 equals 1,268.3, which rounds to 1,268 gallons.
Answer: 28.26 cubic feet. Cylinder volume is 3.14 times 3 squared times 1, which is 3.14 times 9 times 1 equals 28.26.
Answer: 211 gallons. 28.26 times 7.48 equals 211.3, which rounds to 211 gallons.
Answer: 197.82 cubic feet. 169.56 plus 28.26 equals 197.82 cubic feet.
Answer: 25.12 cubic feet. Cone volume is one-third times 3.14 times 2 squared times 6, which is one-third times 3.14 times 4 times 6 equals one-third of 75.36, or 25.12.
Answer: 14.13 cubic feet. Sphere volume is four-thirds times 3.14 times 1.5 cubed. 1.5 cubed is 3.375, times 3.14 is 10.5975, times four-thirds is 14.13.
Answer: 67 cubic feet. 500 gallons divided by 7.48 gallons per cubic foot equals 66.8, which rounds to 67 cubic feet.
Answer: 0.6 feet. The basin's surface area is 3.14 times 6 squared equals 113.04 square feet. 67 divided by 113.04 equals 0.59, which rounds to 0.6 feet deeper.
Answer: Doubling the radius adds more. The radius is squared, so doubling it multiplies the volume by 4 (to 678.24 cubic feet), while doubling the depth only multiplies it by 2 (to 339.12 cubic feet).

Differentiation

Support

Provide the squared and cubed values already worked out (6 squared is 36, 3 squared is 9, 1.5 cubed is 3.375) so students can focus on the multiplication and the conversion. Let students use a calculator and check items 1 through 4 with a partner before moving on.

Extension

Ask students to redesign the sphere on top so its volume is at least double the value from item 7 while keeping a radius of 2 feet or less, and to show the new radius and recalculated volume that make it work.

ELL supports

Provide a labeled diagram of a cylinder, a cone, and a sphere with the radius and height marked on each. Give a small vocabulary card matching each form's name to its formula, and allow the item 10 explanation to be a short sentence or a labeled sketch.