Question

A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is $8cm$ and the total height of teh cup is $11.5cm.$ Find the total surface area of the cup.

Answer 1

Given:

Height of the cylinder $=8cm$

Total height of the cup $=11.5cm$

Height of hemisphere $=11.5-8$

$=3.5cm$

The radius of the hemisphere will be equal to the height of the hemisphere that is $3.5cm.$

Radius, $r=3.5cm$

Now, total surface area of the cup $=$ Curved surface area of cylinder $+$ Curved surface area of hemisphere

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

$=2\pi r(h+r)$

$=2\pi \times 3.5(8+3.5)$

$=7\pi \left(11.5\right)$

$=253c{m}^2$

Hence, the total surface area of the cup is $253c{m}^2.$