Question

Find surface area of a sphere of radius:
(i) 10.5 cm
(ii) 5.6 cm

Answer 1

Hint:
We will use the formula for the surface area of a sphere. We will substitute the values of radius in the formula and perform the calculations to obtain the surface area.
Formulas used: The surface area of a sphere of radius \[r\] is given by \[S.A = 4\pi {r^2}\].

Complete step by step solution:
The sum of areas of all surfaces of a 3-dimensional figure is called its surface area. The surface area of a sphere can be defined as the exact number of square units that will be required to cover the surface of the sphere completely.
The area of a circle with radius \[r\] is \[\pi {r^2}\]. We can say that the surface area of a sphere is 4 times the area of a 2-dimensional circle with the same radius.
1) Let us substitute 10.5 cm for \[r\] in the formula.
\[S.A = 4\pi {\left( {10.5} \right)^2}\]
Simplifying the above expression, we get
\[\begin{array}{l}S.A = 4 \times \dfrac{{22}}{7} \times \dfrac{{105}}{{10}} \times \dfrac{{105}}{{10}}\\\Rightarrow S.A = 1386\end{array}\]
The surface area of a sphere with radius 10.5 cm is 1386 square centimetres.

2) Let us substitute 5.6 cm for \[r\] in the formula.
\[S.A = 4\pi {\left( {5.6} \right)^2}\]
Simplifying the above expression, we get

\[\begin{array}{l}S.A = 4 \times \dfrac{{22}}{7} \times \dfrac{{56}}{{10}} \times \dfrac{{56}}{{10}}\\\Rightarrow S.A = 394.24\end{array}\]

The surface area of a sphere with radius 5.6 cm is 394.2 square centimetres.

Note:
The surface area of a sphere with radius \[r\] contains all the points which are at a distance of \[r\] from the centre of the sphere. A sphere has the lowest surface area for a given volume which is why we find a lot of spherical objects in nature. For example, water droplets, bubbles and celestial bodies like the sun, moon, earth and other planets.