Question

the ratio of surface area of two spheres is 2 : 3 then the ratio of their volume is?plz answer quickly​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER:

Ratio of their volume:

$\frac{2}{3} \sqrt{ \frac{2}{3} }$

GIVEN:

• Ratio of surface area of two spheres is 2 : 3

TO FIND:

• Ratio of their volume.

SOLUTION:

Let the radius of smaller sphere = x

Let the radius of larger sphere = y

Now

Ratio of surface area of two spheres is 2 : 3

$\implies \: \dfrac{4\pi \: x {}^{2} }{4\pi \: y {}^{2} } = \dfrac{2}{3} \\ \\ \implies \: \frac{x {}^{2} }{y {}^{2} } = \frac{2}{3} \\ \\ \implies \: \frac{x}{y} = \frac{ \sqrt{2} }{ \sqrt{3} }$

Now ratio of their volume.

$ratio \: of \: their \: volume \: = \frac{ \frac{4}{3} \pi \: x {}^{3} }{\frac{4}{3} \pi \: y {}^{3}} \\ \\ = (\frac{x}{y} ) {}^{3} \\ \\ = ( \frac{ \sqrt{2} }{ \sqrt{3} } ) {}^{3} \\ \\ = \frac{2}{3} \sqrt{ \frac{2}{3} }$

Ratio of their volume :

$= \frac{2}{3} \sqrt{ \frac{2}{3} }$