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.

• A. $266.11c{m}^3$
• B. $301.12c{m}^3$
• C. $242.36c{m}^3$
• D. $278.34c{m}^3$

Answer 1

Answer: (A)

$266.11c{m}^3$

The volume of wooden toy will the volume of the right circular cone plus the volume of the hemisphere on which it is mounted.

Volume of the cone $=\frac{1}{3}\pi r^{2}h$

Volume of the hemisphere$=\frac{2}{3}\pi r^3$

Here,

$r=$ Radius of the hemisphere or the radius of the cone ; as in this cane the cone is mounted on hemisphere so both's radius will be the same

$h=$ Height of the cone

Given :

$r=4.2cm$

as the total height of the toy is 10.2cm so the height of the cone will be : this total height $-$ radius of the hemisphere.

$h=10.2-4.2=6cm$

Therefore the volume of toy $V:$

$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$

$=\frac{1}{3}\pi {4.2}^2\times 6+\frac{2}{3}\pi {4.2}^3$

$=110.835+155.1695$

$\approx 266.11c{m}^3$ $Ans.$