Question

7. If the diameter of the moon is approximately one fourth of the diameter of the ea find the ratio of their surface areas. ​

Answer 1

Step-by-step explanation:

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

Since the moon and earth are spherical in shape, so the surface area of a sphere of radius r, SA = 4πr2

Let the radius of the earth be R and the radius of the moon be r.

Diameter of the moon = 1/4 × diameter of the earth

Thus, the radius of the moon = 1/4 × radius of the earth [Since, radius = 2 × Diameter]

r = 1/4 × R

r/R = 1/4 ------------ (1)

Now, the surface area of earth = 4πR2

The surface area of moon = 4πr2

The ratio of their surface areas = 4πr2/4πR2

= r2/R2

= (r/R)2

= (1/4)2 [From equation(1)]

= 1/16

The ratio of their surface areas = 1:16

Answer 2

Answer:

16:1

Step-by-step explanation:

$radius \: of \: earth = \frac{d}{2} \\ \\ radius \: of \: moon = \frac{ \frac{d}{4} }{2} = \frac{d}{8} \\ \\ surface \: area \: of \: sphere = \\ 4\pi {r}^{2} \\ \\ 4\pi (\frac{d}{2})^2 = earth \\ \\ = \frac{4\pi {d}^2}{4} \\ \\ moon = 4\pi ({ \frac{d}{8} })^{2} = \frac{4\pi {d}^{2} }{64} \\ \\ ratio = \frac{ \frac{4\pi {d}^{2} }{4} }{ \frac{4\pi {d}^{2} }{64} } \\ \\ \frac{4\pi {d}^{2} } {4} \times \frac{64}{4\pi {d}^{2} } \\ \\ = \frac{64}{4} = \frac{16}{1}$

it is ratio of surface areas of Earth is to moon

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