what is the height of a cone with radius 2?

Question

A solid metal cylinder with radius 2 and height 2 is recast as a solid cone with radius 2.  Find the height of the cone. I need a formula

Answer 1

Volume of cylinder is πr²h=8π.

Volume of cone=⅓πr²h=(4/3)πh=8π. So (4/3)h=8 and h=¾ of 8=6.

If the cylinder dimensions are R and H, and the cone dimensions are r and h, the formula is:

R²H=r²h/3 or 3R²H=r²h. Insert the known values and find the unknown variable: h=3R²H/r².