A hollow sphere of internal and external diameters `4 cm` and `8 cm` respectively is melted into a cone of base diameter `8 cm.` Calculate the height of the cone.

Explanation

External radius of the sphere `= 4 cm`
Internal radius of the sphere `= 2 cm`
Volume of the material of the sphere `= (4)/(3) pi (4^(3) - 2^(3)) cm^(3)`
`= ((224pi)/(3)) cm^(3)`
Radius of the resulting cone, `r = 4 cm`
Let the height of this cone formed be `h` cm
Volume of the cone `= ((1)/(3) pir^(2)h) cm^(3)`
`= ((1)/(3) pi xx 4 xx 4 xx h) cm^(3) = ((16pih)/(3)) cm^(3)`
`:. (16pih)/(3) = (224pi)/(3) rArr h = ((223)/(3) xx (3)/(16)) = 14`
Hence, the height of the cone is `14 cm.`