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Geometry

Volume

Intro

Concept Quizzes

Volume Warmup
Volume - Cuboid
Volume - Cylinder
Volume - Sphere
Volume - Pyramid
Volume - Problem Solving

Challenge Quizzes

Volume: Level 1 Challenges
Volume: Level 2 Challenges
Volume: Level 3 Challenges

Volume: Level 3 Challenges

Three identical tanks are shown above. The spheres in a given tank are the same size and packed wall-to-wall. If the tanks are filled to the top with water, then which tank would contain the most water?

A B C They'll all contain the same amount of water

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by Zandra Vinegar

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A solid sphere of chocolate has a volume of $288\pi$ . The chocolate is then melted down and reshaped into a solid cube. Assume no chocolate was wasted.

Did the sphere have a greater surface area or does the cube?

Useful equations:

Volume of a sphere: $V=\frac{4}{3}\pi r^3$
Volume of a cube: $V=a^3$
Surface area of a sphere: $A=4\pi r^2$
Surface area of a cube: $A=6a^2$

The Sphere The Cube Their surface areas were equal

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by Stewart Feasby

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How many cubes measuring 2 units on one side must be added to a cube measuring 8 units on one side to form a cube measuring 12 units on one side?

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by Yash Singhal

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What is the volume of the octahedron inside this $8 \text{ in}^3$ cube?

4 \text{ in}^3

2 \text{ in}^3

\frac{4}{3} \text{ in}^3

3 \text{ in}^3

1 \text{ in}^3

\frac{8}{3} \text{ in}^3

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by Clara Blackstone

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A chocolate shop sells its products in 3 different shapes: a cylindrical bar, a spherical ball, and a cone. These 3 shapes are of the same height and radius, as shown in the picture. Which of these choices would give you the most chocolate?

$\text{ I. A full cylindrical bar } \hspace{.4cm} \text{ or } \hspace{.45cm} \text{ II. A ball plus a cone }$

A cylindrical bar because it has more volume. A ball plus a cone because the volume of the two is greater than just one. Not enough information. Doesn't matter. Both options have got the same amount.

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by Worranat Pakornrat

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