Question
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.
Solution
Let r1 r2 and r3 cm denate the radii of the base of the cylinder, cone and hemisphere respectively. Then,
r1 = r2 = r3 = `4/3` =2 cm
Let h1 and l cm be the heights of the cylinder and cone respectively. Then,
h = 4cm and l= 2cm
s0, the remaining volume of the cylinder when the toy is inserted into it.
= Volume of the cylinder -(volume of the cone + volume of the hemisphere)
`= pir_1^2h-(1/3pir_2^2l+2/3pir_3^3)`
`=pixx(2)^2xx4-(1/3pixx(2)^2xx2+2/3pixx(2)^3)`
`=16pi-((8pi)/3+(16pi)/3)`
`=16pi-((24pi)/3)`
=16π - 8π
= 8π cm3
