Volume of Spheres and Cones - Solve each problem in terms of pi

Sep 30, 2026

Uploaded by Patrick

Practice problems calculating volumes of spheres and cones in terms of π using given circumference, diameter, radius, and height measures. Spheres use V = 4/3(π)(r^3), while cones use V = 1/3(π)(r^2)(h). Word-based contexts include beads, planets, melons, snow globes, marbles, bowling balls, fish bowls, oranges, ice cream scoops, balloons, funnels, traffic cones, and volcano models. An answer key is included with results expressed as multiples of π.

LanguageEnglish

CategoryExam

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Pages3

Reading Time8 min

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Problems

Spheres and cones volume in terms of π

Answer key

Volume of Spheres and Cones (Word) Name: | Solve each problem in terms of pi. Use V = 4/3(pi)(r^3) for spheres and V = 1/3(pi)(r^2)(h) for cones.
1) A bead is a sphere with a circumference of 18π millimeters. What is the volume of the bead, in cubic millimeters, in terms of pi?
2) A planet model is a sphere with a radius of 3 centimeters. What is the volume of the model, in cubic centimeters, in terms of pi?
3) A melon is a sphere with a circumference of 18π inches. What is the volume of the melon, in cubic inches, in terms of pi?
4) A traffic cone is shaped like a cone with a radius of 2 inches and a height of 9 inches. What is the volume of the traffic cone, in cubic inches, in terms of pi?
5) A snow globe is a sphere with a circumference of 18π centimeters. What is the volume of the snow globe, in cubic centimeters, in terms of pi?
6) A volcano model is shaped like a cone with a radius of 6 inches and a height of
12 inches. What is the volume of the model, in cubic inches, in terms of pi?
7) A bowling ball is a sphere with a circumference of 12π inches. What is the volume of the bowling ball, in cubic inches, in terms of pi?
8) A funnel is shaped like a cone with a radius of 2 centimeters and a height of 15 centimeters. What is the volume of the funnel, in cubic centimeters, in terms of pi?
9) A marble is a sphere with a circumference of 12π millimeters. What is the volume of the marble, in cubic millimeters, in terms of pi?
10) Gwen rolled a snowball into a sphere with a circumference of 12π inches. What is the volume of the snowball, in cubic inches, in terms of pi?
11) A fish bowl is a sphere with a diameter of 12 inches. What is the volume of the fish bowl, in cubic inches, in terms of pi?
12) A water tank is a sphere with a radius of 6 feet. What is the volume of the tank, in cubic feet, in terms of pi?
13) An orange is a sphere with a circumference of 6π centimeters. What is the volume of the orange, in cubic centimeters, in terms of pi?
14) A scoop of ice cream is a sphere with a diameter of 12 centimeters. What is the volume of the scoop, in cubic centimeters, in terms of pi?
15) A balloon is inflated into a sphere with a diameter of 18 inches. What is the volume of the balloon, in cubic inches, in terms of pi? | | | | Answers
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Math
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11-15 | 93 | 87 | 80 | | 73 | 67 | 60 | 53 | 47 | 40 | 33 | | | 27 | 20 | 13 | | 7 | 0 | | | | | | Volume of Spheres and Cones (Word) Name: Answer Key | Solve each problem in terms of pi. Use V = 4/3(pi)(r^3) for spheres and V = | | | | | Answers | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 1/3(pi)(r^2)(h) for cones.
1) A bead is a sphere with a circumference of 18π millimeters. What is the volume of the bead, in cubic millimeters, in terms of pi?
2) A planet model is a sphere with a radius of 3 centimeters. What is the volume of the model, in cubic centimeters, in terms of pi?
3) A melon is a sphere with a circumference of 18π inches. What is the volume of the melon, in cubic inches, in terms of pi?
4) A traffic cone is shaped like a cone with a radius of 2 inches and a height of 9 inches. What is the volume of the traffic cone, in cubic inches, in terms of pi?
5) A snow globe is a sphere with a circumference of 18π centimeters. What is the volume of the snow globe, in cubic centimeters, in terms of pi?
6) A volcano model is shaped like a cone with a radius of 6 inches and a height of
12 inches. What is the volume of the model, in cubic inches, in terms of pi? | | | | | 1. 972π
2. 36π
3. 972π
4. 12π
5. 972π

FAQs

What formulas are used to compute the volumes of spheres and cones in these problems?

Spheres use V = 4/3(π)(r^3). Cones use V = 1/3(π)(r^2)(h).

What measurements are provided for spheres in the word problems?

The problems give either circumference, diameter, or radius for different spherical objects, and you convert those to radius as needed.

How are answers expected to be written?

Answers are written in terms of π, typically as a coefficient multiplied by π (for example, 288π).

Sep 30, 2026

Uploaded by Patrick