Question

The formula for the surface area of a sphere is $SA = 4\pi {r^2}$. If the radius of Mercury is $1550\,miles$. What is its surface area to the nearest square mile?

Answer 1

Hint: In this question, we are given a mercury whose radius is $1550\,miles$. We have to find the surface area to the nearest square miles. We will use the formula $SA = 4\pi {r^2}$ where $SA$ is surface area and $r$ is the radius of the mercury.

Complete step by step answer:
We are given mercury which is in the shape of a sphere whose radius is $1550\,miles$. We have to find the surface area of the mercury. Surface area is defined as the measure of the total area that the surface of the object occupies. The formula for finding the surface area is given by $SA = 4\pi {r^2}$.

We can see in the above figure, the radius of the mercury is $1550\,miles$.
$\Rightarrow r = 1550\,miles$
Hence, the surface area of mercury $= 4 \times \pi \times {(1550)^2}$
Putting the value of $\pi = 3.14$. We get,
$\Rightarrow SA = 4 \times 3.14 \times {(1550)^2}$
On simplification,
$\Rightarrow$$SA = 12.56 \times {(1550)^2}$
$\therefore SA = 30,175,400{(miles)^2}$

Hence, the surface area of mercury is $30,175,400{(miles)^2}$.

Note: In solving these types of problems one should not forget to put units for radius and surface area. Note that a sphere has only normal surface area neither total surface area nor lateral surface area. Almost all other $3D$ objects have two types of surface areas.