A hemisphere of lead of radius 8cm is cast into a right circular cone of base radius 6cm. Determine the height of the cone, correct to two places of decimal.

Explanation

Let height of the cone be h.
given , radius of the base of the cone = 6cm
`therefore` Volume of circular cone `=(1)/(3) pir^(2)h` ` =(1)/(3) pi(6)^(2) h =(36 pih)/(3) - 12 pi h cm^(3)`
Also, given radius of the hemisphere = 8 cm
`therefore ` Volume of the hemisphere `= (2)/(3)pi r^(3) = (2)/(3) pi (8)^(2) = (512 xx 2 pi )/(3) cm^(3)`
According to the question, ltbgt Volume of the cone = Volume of the hemisphere
`rArr" " 12pi h = (512 xx 2pi)/(3)`
`therefore" "h = (512 xx 2 pi)/(12 xx 3 pi) = (256)/(9) = 28.44 cm`