Question

Mayank made a birdbath for his garden in the shape of a cylinder with a hemispherical depression at one end (see Fig.). The height of the cylinder is $1.45m$ and its radius is $30cm$. Find the total surface area of the birdbath. (Take $\pi$ = $\frac{22}{7}$)

Answer 1

Given: The height of the cylinder is $1.45m$ and its radius is $30cm$.

Let $h$ be height of the cylinder, and $r$ the common radius of the cylinder and hemisphere. Then,

The total surface area of the bird-bath $=$ CSA of cylinder $+$ CSA of hemisphere $+$ Area of the circle in bottom

$=2\pi rh+2\pi r^2$

$=(2\times \frac{22}{7}\times 30\times 145)+(2\times \frac{22}{7}\times {30}^2)[\because 1.45m=145]$

$=\frac{191400}{7}+\frac{39600}{7}$

$=\frac{231000}{7}$

$=33000c{m}^2$

$=3.3m^2$

Hence, the total surface area of the birdbath is $3.3m^2$.