A solid cone and a solid cylinder have bases of the same radius and have equal volumes. The cylinder is 8 cm tall. How tall is the cone?

2\frac{2}{3}

cmCorrect answerYour answer8 cmCorrect answerYour answer16 cmCorrect answerYour answer24 cmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Equal volumes: $\frac{1}{3}\pi r^2 H = \pi r^2 \times 8$ .
Cancel πr²: $H \div 3 = 8$ , so $H = 24$ cm.

Worth noting

A cone holds one-third of the cylinder with the same base and height, so it needs three times the height to match. $8/3$ cm divides instead of multiplying.

Concept: Cone versus cylinder on the same base
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCylinders, cones and spheres

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A solid cone and a solid cylinder have bases of the same radius and have equal volumes. The cylinder is 8 cm tall. How tall is the cone?

Explanation