Question

Volume of two spheres are in the ratio 64 | 27, find
the ratio of their surface areas.​

Answer 1

Answer:

Let the radius of two spheres be Ready and r.The ratio of their volumes

={4/3.π.R^3}/{4/3.π.r^3} = 64/27

So R^3/r^3 =64/27.

R/r= 4/3.

Ratio of their surface areas

= 4πR^2/4πr^2 =R^2/r^2 = (R/r)^2

=(4/3)^2 = 16/9.

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Answer 2

Given :

Volume of two spheres are in the ratio 64 : 27,

To find:-

find the ratio of their surface areas.

Solution :-

$\rm Volume\: of\:sphere = \dfrac{4}{3} \pi r^3$

$\implies \rm \dfrac{Volume\:of\:sphere(1)}{Volume\:of\:sphere(2)} = \dfrac{64}{27}$

$\implies \rm\dfrac{\dfrac{4}{3}\pi r_1^3}{\dfrac{4}{3}\pi r_2^3} = \dfrac{64}{27}$

$\implies \rm \dfrac {r_1^3}{r_2^3} = \dfrac{64}{27}$

$\implies \rm \dfrac {r_1}{r_2} = \cancel\dfrac{64}{27}$

$\implies \rm \dfrac {r_1}{r_2} = \dfrac{4}{3}$

Ratio of areas of both spheres

Area of sphere = 4πr²

$\implies \rm \dfrac{Area\:of\:sphere(1)}{Area\:of\:sphere(2)} = \dfrac{4\pi r_1^2}{4 \pi r_2^2}$

$\implies \rm \dfrac{4\pi r_1^2}{4 \pi r_2^2} = \dfrac {r_1^2}{r_2^2}$

$\implies \rm \left(\dfrac { r_1}{r_2}\right)^2 = \dfrac{4^2}{3^2} = \dfrac{16}{9}$

Therefore,

Ratio of their surface areas = $\bf\dfrac{16}{9}$