The circus ringleader, Ms. Evelyn, wants all the employees to have miniature cakes in the shape of either a circus ball or a clown hat. She wants the clown hat dessert and the circus ball dessert to be the same volume. The radius of both cake pieces will be 3 in. What must the height of the clown hat cake be in order for the two cakes to be equal in volume? Round to the nearest hundredth if necessary. Explain or show your work.

Question

Brandi

Mathematics

30 November, 21:22

The circus ringleader, Ms. Evelyn, wants all the employees to have miniature cakes in the shape of either a circus ball or a clown hat. She wants the clown hat dessert and the circus ball dessert to be the same volume. The radius of both cake pieces will be 3 in. What must the height of the clown hat cake be in order for the two cakes to be equal in volume? Round to the nearest hundredth if necessary. Explain or show your work.

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Shaw · Answer 1

Im assuming the hat is a cylinder and the ball is a sphere

volume of cylinder (hat) = pi * r^2 * h

volume of sphere = 4/3 pi r^3

plug in your radius to first find volume of sphere

4/3 * pi * 3^3 = 36pi

set that equal to the formula for cylinder and solve

36pi = pi * 3^2 * h

36pi = 9pi * h

36pi / 9 pi = h

4=h