Question

The surface area of two sphere are in the ratio 16:9 find their volume

Answer 1

$Let \: R \: and \:r \: are \: radii \: of \: two$

$spheres$

$\blue { Ratio \: of \: surface \: area = 16:9}$

$\implies \frac{4 \pi R^{2}}{4 \pi r^{2}} = \frac{4^{2}}{3^{2}}$

$\implies \Big( \frac{R}{r}\Big)^{2} = \Big(\frac{4}{3}\Big)^{2}$

$\implies \frac{R}{r}= \frac{4}{3}\: --(1)$

$\red{ Ratio \:of \: volume} = \frac{ \frac{4}{3} R^{3}}{ \frac{4}{3} r^{3}}$

$= \Big( \frac{R}{r}\Big)^{3}$

$= \Big( \frac{4}{3}\Big)^{3}$

$= \frac{64}{27}$

$= 64 : 27$

Therefore.,

$\red{ Ratio \:of \: volumes \: of \: spheres }$

$\green { = 64 : 27}$

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