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

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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


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.


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

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


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