Question

Find the surface area of a sphere of radius $14\,cm$.

Answer 1

Hint: The volume of a sphere is the capacity that the sphere has. It defines the volume of a liquid or any matter that the sphere can hold. The shape of the sphere is round and three -dimensional. We have to find the volume of a sphere when we are given the radius of the same. So, we will substitute the value of radius provided in the problem into the formula for surface area of the sphere as $4\pi {r^2}$.

Complete step-by-step answer:

The volume V of the sphere depends on the diameter or the radius of the sphere since if we take the cross-section of the sphere, it is a circle. So, the volume of the sphere depends upon the radius of the sphere and that’s why the formula of the volume of the sphere consists of the radius of the sphere as a parameter.
So, we are given the radius of the sphere as $14\,cm$.
We know that the formula for surface area of a sphere is $4\pi {r^2}$.
So, substituting the value of the radius of the sphere, we get,
Surface area of sphere $ = 4\pi {\left( {14cm} \right)^2}$
We also know that a square of $14$ is $196$. So, computing the square of the term, we get,
$ = 4\pi \left( {196} \right)c{m^2}$
Now, substituting the value of $\pi $ as $\left( {\dfrac{{22}}{7}} \right)$, we get,
$ = 4 \times \dfrac{{22}}{7} \times \left( {196} \right)c{m^2}$
Cancelling common factors in numerator and denominator, we get,
$ = 4 \times 22 \times 28\,c{m^2}$
Simplifying the calculations, we get,
$ = 88 \times 28c{m^2}$
$ = 2464\,c{m^2}$
So, the correct answer is “$2464\,c{m^2}$”.

Note: The sphere is defined as the three-dimensional round solid figure in which every point on its surface is equidistant from its centre. The fixed distance is called the radius of the sphere and the fixed point is called the centre of the sphere. We must know the formula for calculating the surface area of a sphere in terms of its radius. Utmost care should be taken while substituting the value of $\pi $ into the equation.