A metal solid cylinder of radius 6 cm and length 12 cm is ,melted and recast into another solid cylinder of length 3 cm.

Question

A. Find the base radius of the new cylinder.
B. Find the change in total surface area in terms of 3.14.

Answer 1

volume of old = π r^2 h
= π(36)(12)= 432π

this must stay the same

we know the new h, but not the r

new volume = 3π r^2

so 2π r^2 = 432π
divide by 2π
r^2 = 216
r =√216 = appr 14.7

SA = 2πr^2 + 2πrh

old SA = 2π(36) + 2π(6)(12) = 216π
new SA = 2π(√216)^2 + 2π(√216)(3)
= 432π + 6√216π

change = 432π + 36√6π - 216π
= 216π + 36√6 π

Answer 2

Thanks