# NCERT Solutions Class 9 Mathematics Solutions for Surface Areas and Volumes - Exercise 13.4 in Chapter 13 - Surface Areas and Volumes

Question 7 Surface Areas and Volumes - Exercise 13.4

The diameter of the moon is approximately one-fourth of the diameter of the earth.

Find the ratio of their surface areas.

If the diameter of the earth is said d, then the diameter of the moon will be d/4 (as per given statement)

Radius of moon = ½ × d/4 = d/8

\begin{aligned} &\text { Ratio of their Surface areas }=\frac{4 \pi\left(\frac{d}{8}\right)^{2}}{4 \pi\left(\frac{d}{2}\right)^{2}}=4 / 64=1 / 16\\ &\text { The ratio between their surface areas is } 1: 16 \text { . } \end{aligned}

Video transcript
"hello students welcome to lido q a video session i am seth your math tutor and question for today is the diameter of the moon is approximately one-fourth of the diameter of the earth find the ratio of their surface areas if the diameter of the earth is said to be d then the diameter of the moon will be d upon 4 that is the meaning of our first sentence in the question so here if diameter of earth is d then diameter of the moon is d upon 4 now radius of the earth will be equal to b upon 2 as we have considered diameter is d radius will be half of the diameter and hence you can say that the radius of the moon is d upon it so it was the diameter of the moon as d by four so d upon four upon 2 that is d upon 8 so now we have radius of the moon and radius of the earth surface area of the moon can be given by 4 pi r square that is radius of the moon so here surface area formula write down as a general surface area of sphere 4 pi r square hence if you take here surface area of moon and surface area of earth and then you find ratio then your answer comes out to be like this surface area of moon divided by surface area of earth that is our ratio so for moon we have radius d by d by eight so d by eight square and for earth we have radius d by two hence we can now proceed further to find ratio so required ratio that is ratio will be equal to d by 8 square upon d by 2 square that is 4 upon 64 so ratio comes out to be 1 upon this is the fraction you can convert this fraction in ratio as ratio is equal to 1 is to 16 so ratio between their surfaces area are 1 is to 16. this is our required ratio if you have any query you can drop down below in our comment section and subscribe to lido for more such q a thank you for watching"
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