Question

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 inches. what must the height of the clown hat cake be in order for the two cakes to be in equal volume? round to the nearest hundredth if necessary. explain or show your work. (Please show procedure. The clown hat is a cone and the circus ball is a sphere)

Answer 1

clown hat is a cone
circus ball is a sphere

volumes of each
Vcone=(1/3)hpir^2
Vsphere=(4/3)pir^3

r=3
find Vsphere since we have enough info to solve that, (need height for Vcone)

Vsphere=(4/3)pi3^3
Vsphere=(4/3)pi27
Vsphere=36pi
leave in terms of pi

Vcone=Vsphere is given
and r=3
so
36pi=(1/3)hpi3^3
36pi=(1/3)hpi9
36pi=3hpi
divide both sides by pi
36=3h
divide by 3
12=h

height must be 12 inches tall of clown hat cake