A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the total height of the solid are 21cm, 25.2 cm respectively, then its volume is

Let $r\text{and}h$  are radius and height of cylinder.

Diameter of the hemisphere $=21$

Radius of hemisphere $\left(r\right)=\frac{\left(21\right)}{2}=10.5$

Total height of the solid shape $=25.5$

Radius of hemisphere $+$  height of the cylinder $=25.5$

$10.5+h=25.5$

$h=15\text{cm}$

To find the volume of the solid shape we have to find the sum of volume of hemisphere and volume of cylinder

Volume of solid toy$=$ Volume of hemisphere $+$ Volume of cylinder

$=\left(\frac{2}{3}\right)\pi r^3+\pi r^{2}h=\pi r^2\left[\left(\frac{2}{3}\right)r+h\right]$

$=\left(\frac{22}{7}\right)\times {\left(10.5\right)}^2\left[\left(\frac{2}{3}\right)10.5+15\right]$

$=\frac{22}{7}\times \left(10.5\right)\times \left(10.5\right)\left[2\left(3.5\right)+15\right]$

$=22\left(1.5\right)\times \left(10.5\right)[7+15]=33\times \left(10.5\right)\left[22\right]$

$=7623{\text{cm}}^3$

Volume of solid shape $=7623{\text{cm}}^3$