SOLUTION: Merion forms a ball of clay with a radius of 2 in. He then reforms the clay into a cylinder of radius 3 in. What is the height of the cylinder?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Merion forms a ball of clay with a radius of 2 in. He then reforms the clay into a cylinder of radius 3 in. What is the height of the cylinder?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 850358: Merion forms a ball of clay with a radius of 2 in. He then reforms the clay into a cylinder of radius 3 in. What is the height of the cylinder?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of Sphere: %284%2F3%29pi%2Ar%5Bs%5D%5E2
Volume of Cylinder: h%2Api%2Ar%5Bc%5D%5E2
-
Subscripts are s for the sphere, and c for the cylinder and these radii may be different values.

Sphere: Radius is the given value so no unknowns here. r[s] is known because it is given.
Cylinder: The radius, r[c] here is also given, so it is also known. The unknown is h, the height, which is what you want to solve for.

The volumes of the sphere and the cylinder reformed from it are equal. This means symbolically that highlight%28%284%2F3%29pi%2Ar%5Bs%5D%5E2=h%2Api%2Ar%5Bc%5D%5E2%29.
SOLVE FOR h.
highlight%28h=%28%284%2F3%29pi%2Ar%5Bs%5D%5E2%29%2F%28pi%2Ar%5Bc%5D%5E2%29%29 and you need to simplify this.
SUBSTITUTE THE GIVEN VALUES.