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

## Question

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 \(\begin{align}= 4 \pi\left(\frac{r}{4}\right)^{2} \end{align}\)

Therefore, Ratio of their surface area,

\[\begin{align}&=\frac{\text { Surface area of the moon }}{\text { Surface area of the earth }}\\&=\frac{4 \times \pi \times r^{2}}{4 \times \pi \times 4 \times 4 \times r^{2}}\\&=\frac{1}{16}\end{align}\]

**Answer:**

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