A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.

Explanation

Let OAB be the cone and ACB be the hemisphere, having the same base AB. Let the right given solid. Radius of each of the cone , cylinder and hemisphere r= 2 cm.
Height of the cylinder ,
H=h+r =(2+2) cm = 4 cm
Volume of the toy
= (volume of the hemisphere )+( volume of the cone )
`=2/3 pi r^3 + 1/3 pi r^2h `
`=(2/3 pi xx 2^3 + 1/3 pi xx 2^2 xx 2 )cm^3`
`=((16 pi)/(3)+(8 pi )/3)cm^3 = 8 pi cm^3`
Volume of the cylinder `= pi r^2 H`
`=( pi xx 2^2 xx 4 ) cm^3 = (16 pi )cm^3`
Required volume = volume of the cylinder - volume of the toy
`=(16 pi - 8 pi ) cm^3 = 8 pi cm^3`
`= (8 xx 3.14 ) cm^3 = 25.12 cm^3`
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