A right circular cone of height 81cm and radius of the base 16cm is melted and recast into a right circular cylinder of height 48cm. find the radius of the base of the cylinder.
Given,
Height of cone, h = 81 cm
Radius of cone, r = 16 cm
∵ Volume of cone = 1/3TTr2h
= 1/3TT(16)2(81)
= 6912TT cm3
Now,
Height of cylinder, h = 48 cm
Radius of cylinder, r = ?
Volume of cylinder = TTr2h
= TTr2(48)
= 48TTr2 cm3
Now,
Volume of cylinder = Volume of cone
48TTr2 = 6912TT
r2 = 144
r = √144 = 12 cm
So, radius of cylinder = 12 cm