Question

Find the surface area of a sphere of diameter $14{\text{ cm}}$ (in ${\text{c}}{{\text{m}}^2}$)

Answer 1

Hint: First determine the radius of the sphere by applying the formula $r = \dfrac{d}{2}$, where $d$ and $r$ are diameter and radius of the sphere respectively. Then apply the formula of surface area of the sphere i.e. $A = 4\pi {r^2}$ to find the answer. Use the value of $\pi $ as $\dfrac{{22}}{7}$.

Complete step-by-step answer:
According to the question, the diameter of the sphere is $14{\text{ cm}}$. We have to calculate its surface area.
We know that the radius is half of the diameter as shown below:
$ \Rightarrow r = \dfrac{d}{2}$, where $d$ and $r$ are diameter and radius of the sphere respectively.
Applying this formula to find the radius, we’ll get:
$
   \Rightarrow r = \dfrac{{14}}{2}{\text{ cm}} \\
   \Rightarrow r = 7{\text{ cm}} \\
 $
Hence the radius of the sphere is $7{\text{ cm}}$.
Now, we also know that the formula for surface area of a sphere is given as:
$ \Rightarrow A = 4\pi {r^2}$
Putting the value of radius calculated above, we’ll get:
$ \Rightarrow A = 4\pi \times 7 \times 7$
Simplifying it further by substituting $\pi = \dfrac{{22}}{7}$, we’ll get:
$
   \Rightarrow A = 4 \times \dfrac{{22}}{7} \times 7 \times 7{\text{ c}}{{\text{m}}^2} \\
   \Rightarrow A = 4 \times 22 \times 7{\text{ c}}{{\text{m}}^2} \\
   \Rightarrow A = 616{\text{ c}}{{\text{m}}^2} \\
 $

Thus the surface area of the sphere is $616{\text{ c}}{{\text{m}}^2}$.

Note: If the volume of the sphere is asked instead, this can be calculated using the formula of volume of sphere:
$ \Rightarrow V = \dfrac{4}{3}\pi {r^3}$
While the surface area of the sphere is proportional to the square of the radius i.e. ${r^2}$, the volume is proportional to the cube of the radius (${r^3}$) instead. Hence if the radius of a sphere is doubled, its surface area will become 4 times but the volume will become 8 times of the initial value.