Question

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

Answer 1

Total height of the solid = 9.5 cm
Radius of the cone = Radius of the hemisphere = r = 3.5 cm

Radius of the hemisphere = height of hemisphere = 3.5 cm

Height of cone,( h) = total height of the solid - height of the hemisphere

h = 9.5 - 3.5 cm
h of cone = 6cm

The volume of the solid = volume of cone + volume of the hemisphere

$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$
$=\frac{1}{3}\pi r^2(h+2r)$
$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times (6+2\times 3.5)$
$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times (6+7)$
$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times \left(13\right)$
$=\frac{1}{3}\times 22\times .5\times 3.5\times \left(13\right)$
$=\frac{500.5}{3}$
$=166.83c{m}^3$

Hence, the volume of the solid is $166.83c{m}^3$