A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy. [4 MARKS]
Concept: 1 Mark
Formula: 1 Mark
Application: 2 Marks
VO′=10.2 cm, OA=OO′=4.2 cm
Let r be the radius of the hemisphere and h be the height of the conical part of the toy.
r=OA=4.2 cm
h=VO=VO′−OO′=(10.2−4.2) cm=6 cm
Volume of the wooden toy
= Volume of the conical part + Volume of the hemispherical part
=(13πr2h+2π3r3)cm3
=πr23(h+2r)cm3
=13×227×4.2×4.2×(6+2×4.2)cm3
=13×227×4.2×4.2×14.4 cm3=266.11 cm3