Question

If the surface areas of of two spheres are in the ratio of 4 : 25, then the ratio of their volumes are

Answer 1

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Answer 2

Answer:

$\dfrac{Volume\ of\ first\ sphere}{Volume \ of\ second\ sphere}=\dfrac{8}{125}$

Explanation:

Since we know that the surface area of sphere is $4\pi r^{2}$

Assume $r_{1}$ and $r_{2}$ are the radius of two spheres.

So,as per the given condition

$\dfrac{S.A\ of\ first\ sphere}{S.A\ of\ second\ sphere}=\dfrac{4\pi r_{1} ^{2}}{4\pi r_{2} ^{2}}$

$\dfrac{4\pi r_{1} ^{2}}{4\pi r_{2} ^{2}} =\dfrac{4}{25}$

$\dfrac{r^{2} _{1}}{r^{2} _{2}}=\dfrac{4}{25}$

$\dfrac{r_{1}}{r_{2}}=\dfrac{2}{5}$

$r_{1}:r_{2}=2:5$

$r^{3} _{1}:r^{3} _{2}=8:125$

$\dfrac{r^{3} _{1}}{r^{3} _{1}}=\dfrac{8}{125}$

Since we know that the volume of the sphere is given by $4\pi r^{3}$

So, ration of volume of two spheres are given by,

$\dfrac{Volume\ of\ first\ sphere}{Volume \ of\ second\ sphere}=\dfrac{4\pi r_{1} ^{3}}{4\pi r_{2} ^{3}}=\dfrac{8}{125}$