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Question

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]

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Solution

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=VOOO=(10.24.2) 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


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