SOLUTION: a metal sphere with a radius of 3 cm is melted down and formed into a cylinder with a radius of 2 cm. Calculate the height of the cylinder. The metal cylinder is then melted down a

Algebra ->  Bodies-in-space -> SOLUTION: a metal sphere with a radius of 3 cm is melted down and formed into a cylinder with a radius of 2 cm. Calculate the height of the cylinder. The metal cylinder is then melted down a      Log On


   

Question 889516: a metal sphere with a radius of 3 cm is melted down and formed into a cylinder with a radius of 2 cm. Calculate the height of the cylinder. The metal cylinder is then melted down and formed into a cone with a radius of 1 cm. Calculate the height of the cone.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are asking two related questions, but I will help with the second one.

Volume of a cone, %281%2F3%29h%2Api%2Ar%5E2.
Volume of sphere, %284%2F3%29pi%2Ar%5E3.

The volumes of the cone and sphere will be equal. Just fill what is known and solve for what is unknown, one variable, the height of the cone.

%284%2F3%29pi%2A%283%5E3%29=%281%2F3%29h%2Api%281%5E2%29
%284%2F3%293%5E2%2Api=h%281%2F3%29%2A1%2Api
Multiply by 3, divide by pi, BOTH SIDES
4%2A3%2A3=h
highlight%28h=36%29