Question

Wvolume of 2 spheres are in ratio 64:27.Find the ratio of surface area

Answer 1

$\boxed{\boxed{\mathbf{\frac{16}{9}}}}$
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Let the 2 radii of the spheres be $r_1$ and $r_2$
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We know that,

Volume of a sphere = $\frac{4}{3} \pi r^3$

So, the Ratio of volume of spheres would be :

$\LARGE\mathsf{\frac{\frac{4}{3} \pi r^3_1}{\frac{4}{3} \pi r^3_2} = \frac{64}{27}}$

Cancelling $\mathsf{\frac{4}{3}}$ and $\mathsf{\pi}$ from numerator and denominator , We get,

=> $\LARGE\mathsf{\frac{r^3_1}{r^3_2} = \frac{64}{27}}$

Taking out cube roots of both sides,

$\boxed{\mathsf{\frac{r_1}{r_2} = \frac{4}{3}}}$
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Now,

So, $\mathsf{r_1 = 4 \: and \: r_2 = 3}$

We know that,

Surface are of Sphere = $\mathsf{4 \pi r^2}$

So, the ratio of Surface area of 2 spheres would be :

$\LARGE\mathsf{\frac{4 \pi r^2_1}{4 \pi r^2_2}}$

Cancelling 4 and $\mathsf{ \pi }$ from numerator and denominator, We get,

$\LARGE\mathsf{\frac{r^2_1}{r^2_2} = \frac{4^2}{3^2}}$

=> $\LARGE\mathsf{\frac{16}{9}}$

Hence, the ratio of Surface area of Spheres = $\LARGE\mathsf{\frac{16}{9}}$.

Answer 2

volume ratio = 64 : 27
R^3 : r ^ 3 = 64 : 27
R : r= 4 : 3
now, area ratio = (2πR^2) / ( 2πr^2)
R^2 / r^ 2 = 4^2 : 3^2= 16 : 9