A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere with same radius. 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. (Take π= 227)

Given the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm.
Length of the conical part will be

10.2 - 4.2 = 6 cm

Volume of a hemisphere of radius 'r'

= \frac{2}{3} π r^{3}

Volume of a cone

= \frac{1}{3} π r^{2} h

, where r is the radius of the base of the cone and h is the height.
Volume of the toy

=

Volume of the hemispherical part

+

Volume of conical part

\Rightarrow \frac{2}{3} ​ π r^{3} + \frac{1}{3} π r^{2} h

\Rightarrow \frac{1}{3} ​ π r^{2} (2 r + h)

\Rightarrow = \frac{1}{3} ​ \times \frac{22}{7} \times (4.2)^{2} \times (2 \times 4.2 + 6)

\Rightarrow 266.112 c m^{3}

Therefore, the volume of the wooden toy

266.112 c m^{3}

.
Hence, the correct option is 3.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere with same radius. 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. (Take $π$ = $\frac{22}{7}$ )