Question

The diameter of the moon is approximately one-fourth of the diameter of the earth
What fraction of the volume of the earth is the volume of the moon?
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Answer 1

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➠ The diameter of the moon is approximately one-fourth of the diameter of the earth . What fraction of the volume of the earth is the volume of the moon?

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❏ Sphere is 3-dimensional shape which closely resemble shape of a marble or a playing ball.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed {\bold {\orange {\mathtt {\longmapsto Volume \; of \; Sphere = \dfrac{4}{3}\pi r^2 }}}}$

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❏ Usually all planets are considered to be sphere in fact their real shape may/may not be sphere. But for our easy calculations in mathematics we consider them sphere.

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❏ If the ratio of two diameters are (x : y) then  the ratio of radius will be same or equal to (x : y).

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❏ Radius of moon =  ¹⁄₄ × (Radius of Earth)

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Let's Start !

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❖ Here is your answer :)

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$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{\frac{4}{3} \pi {(r_{moon})}^{3} }{\frac{4}{3} \pi {(r_{earth})}^{3} }$

$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{{(r_{moon})}^{3} }{{(r_{earth})}^{3} }$

$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{{(\frac{1}{4} \times r_{earth})}^{3} }{{(r_{earth})}^{3} }$

$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{{\frac{1}{64} \times (r_{earth})}^{3} }{{(r_{earth})}^{3} }$

$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{1}{64} \times \dfrac{{(r_{earth})}^{3} }{{(r_{earth})}^{3} }$

$:\implies \dfrac{Volume \; of \; Moon}{Volue \; of \; Earth} = \dfrac{1}{64}$

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$\boxed {\bold {\red{\mathtt {: \longmapsto \; Volume \; of \; Moon = \frac{1}{64} \times Volume \; of \; Earth } } } }$

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$\boxed{\boxed{\bold{\therefore Volume \; of \; Moon = \frac{1}{64} \times Volume \; of \; Earth }}}$

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Hope this helps u.../

【Brainly Advisor】