# Ex.13.4 Q7 Surface Areas and Volumes Solution - NCERT Maths Class 9

Go back to  'Ex.13.4'

## Question

Q7. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

## Text Solution

Reasoning:

Surface of the sphere having radius $$r$$ is equal to the $$4$$ times are of the circle having radius $$r.$$ \begin{align}S = 4\pi {r^2} \end{align}

What is known?

Ratio between the diameter of the moon and earth.

What is unknown?

Ratio of the surface areas.

Steps:

Let the diameter of the earth be $$2r.$$

Radius of the earth in $$= r$$

Radius of the moon is $$= \frac{r}{4}$$

Surface area of the earth $$= 4\pi \rm{r^2}$$

Surface area of the moon $$= 4 \pi\left(\frac{r}{4}\right)^{2}$$

\begin{align}\text{∴ Ratio of their surface area} &=\frac{\text { Surface area of themoon }}{\text { Surface area of the earth }}\\&=\frac{4 \times \pi \times r^{2}}{4 \times \pi \times 4 \times 4 \times r^{2}}\\&=\frac{1}{16}\end{align}

\begin{align}\text{Ratio of their surface area = 1:16}\end{align}