Question

the diameter of the moon is approximately one fourth of the diameter of the earth find the ratio of their surface areas​

Answer 1

Answer:----PLEASE MARK MY ANSWER AS BRAINLIEST----

let diameter of earth=x  [radius=x/2]---------------------r1

hence, diameter of moon= x/4  [radius= x/4÷2= x/8]----------------------r2

surface area of sphere = 4πr²

ratio of surface area= 4πr1² / 4πr2²

[4π will get cancelled] →   (r1)²/ (r2)²

= (x/8)² ÷ (x/2)²

=(x²/64) ÷ (x²/4)

=(x²/64) × (4/x²)    [x² gets cancelled out]

=4/64

=1/16

hence, ratio= 1:16

hope it helps you...

----PLEASE MARK MY ANSWER AS BRAINLIEST----

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Ratio of diameter of Moon : Earth = 1 : 4

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Ratio of surface area of Moon : Earth = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Let the diameter be x and 4x

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$\sf{\red{\boxed{\bold{Radius = \dfrac{Diameter}{2}}}}}$

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Therefore radius is x/2 and 4x/2

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$\sf{\red{\boxed{\bold{Surface\: Area = 4\times \pi \times r^2}}}}$

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$\sf : \implies\: {\bold{ Surface\: area\: of \: Moon : Surface \: area \: of \: earth }}$

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$\sf : \implies\: {\bold{ 4\times\dfrac{22}{7} \times (\dfrac{x}{2})^2 : 4\times\dfrac{22}{7} \times (\dfrac{4x}{2})^2}}$

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$\sf : \implies\: {\bold{ \dfrac{22}{7} \times (\dfrac{x}{2})^2 : \dfrac{22}{7} \times (\dfrac{4x}{2})^2}}$

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$\sf : \implies\: {\bold{ (\dfrac{x}{2})^2 : (\dfrac{4x}{2})^2}}$

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$\sf : \implies\: {\bold{ \dfrac{x^2}{4} : (2x)^2}}$

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$\sf : \implies\: {\bold{ \dfrac{x^2}{4} : 4x^2}}$

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$\sf : \implies\: {\bold{ \dfrac{\dfrac{x^2}{4}}{4x^2}}}$

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$\sf : \implies\: {\bold{ \dfrac{\dfrac{x^2}{4}}{\dfrac{1}{4x^2}}}}$

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$\sf : \implies\: {\bold{ \dfrac{x^2}{16x^2}} }$

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$\sf : \implies\: {\bold{ \dfrac{1}{16}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Ratio of surface area of moon : earth = 1 : 16