Question

A hole cylinder iron pipe as of length 40cm its internal and external radii are 4cm and 12 cm it is melted and recasted into solid cylinder and length 20 cm find the radius of new solid

Answer 1

volume of cylinder=πh(R²-r²)
                          =5120π
5120π=20πr²
5120=20r²
√256=r
⇒r=16

Answer 2

Volume of hollow cylinder = πh(r1²-r2²)
= π * 40 * (12²-4²)
= π * 40 *128
=5120π cm³

Volume of solid cylinder = π r² h = volume of hollow cylinder
π r² 20 = 5120 π
r² = 5120/20
r² = 256
r = √256
r = 16 cm