Question

A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm. Find the outer curved surface area of the bowl.

Answer 1

Hint: Outer radius of a hollow hemisphere is the sum of the inner radius and the thickness.Outer curved surface area of a hollow hemisphere is $2\pi r^2$ where ‘r’ is the outer radius of the hemisphere and ${}^{\prime }{\pi }^{\prime }$ is equal to 22/7 or 3.14.

Complete step-by-step answer:

We are given that the hemispherical bowl is made of steel which has thickness 0.25cm and the inner radius of the bowl is 5cm.
Outer radius of the bowl = inner radius of the bowl + thickness of the bowl
$r_2=r_1+t$ , where ‘ $r_2$’ is the outer radius, ‘ $r_1$’ is the inner radius and t is the thickness.

$r_2=5+0.25$
$r_2=5.25$cm
We obtained the outer radius of the bowl.
Outer curved surface area of the bowl where outer radius is $r_2$= $2\pi {r_2}^2$
$$\begin{gathered} =2\times \pi \times r_2\times r_2 \\ =2\times {\displaystyle \frac{22}{7}}\times 5.25\times 5.25 \\ ={\displaystyle \frac{2\times 22\times 5.25\times 5.25}{7}} \\ ={\displaystyle \frac{1212.75}{7}} \\ =173.25c{m}^2 \end{gathered}$$
Outer curved surface area of the steel bowl with inner radius 5cm and thickness 0.25cm is 173.25 square centimeters.


Note: A hemisphere is defined as a three-dimensional shape that's half of a sphere with one flat, circular side. We can find various real-life examples of the hemispheres such as our planet Earth can be divided into two segments which are southern & northern hemispheres. The Hemispheres can either be of a solid type or can be hollow. Total Surface area of a hollow hemisphere is different from the total surface area of a solid hemisphere. Do not confuse a solid hemisphere with a hollow hemisphere. A hollow hemisphere has two radii i.e. inner radius and outer radius and two areas i.e. inner curved surface area and outer curved surface area.