If a right circular cone of height 15 cm and of diameter 30 cm is made from a wooden sphere of radius 15 cm , then percent of wood will be lost ?

Explanation

The radius of the sphere = 15 cm
` :. ` the volume of the sphere `= 4/3 pi xx (15)^(3) `cc.
Now, the radius of the cone = ` 30/2` cm = 15 cm ` [ :' ` diameter = 30 cm ]
and the height of the cone = 15
` :. ` the volume of the cone ` = 1/3 pi xx (15)^(2)xx 15 ` cc
` = 1/3 pi xx (15)^(3) ` cc
` :. ` the lost wood ` { 4/3 pi xx (15)^(3) - 1/3 pi xx (15)^(3) } ` cc
` = ( 4/3 - 1/ 3 ) pi xx ( 15)^(3)" cc" = pi xx (15)^(3) " cc "`
` :. ` the percent of the lost wood ` = (pixx(15)^(3))/(4/3 pi xx (15)^(3)) xx 100 % = 75 % `
Hence the required percentage = 75%