Question

A solid wooden toy is in the form of a cone surmounted on a hemisphere. If the radii of the hemisphere and the base of the cone are $3.5\text{cm}$ each and the total height of the toy is $17.5\text{cm}$, then find the volume of wood used in the toy. Use $\pi =\frac{22}{7}$

Answer 1

Hemispherical portion:

Radius $r=3.5\text{cm}$

Conical portion:

Radius $r=3.5\text{cm}$

Heignt, $h=17.5-3.5=14\text{cm}$

Volume of the wood $=$ Volume of the hemisphere $+$ Volume of the cone

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

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

$=\frac{22}{7}\times \frac{3.5\times 3.5}{3}\times (2\times 3.5+14)$

$=269.5{\text{cm}}^3$

Hence, the volume of the wood used in the toy is equal to $269.5{\text{cm}}^3$