Question

The ratio of volumes of two spheres is 8: 27 then write the ratio of their surface areas

Answer 1

SOLUTION:-

Given:

The ratio of volumes of two spheres is 8:27.

So,

We know that, Volume of spheres;

$= > \frac{4}{3} \pi {r}^{3}$

Let r1 & r2 be the radii of first sphere & second sphere respectively.

Therefore,

$= > \frac{4}{3} \pi(r1) {}^{3} \ratio \frac{4}{3} \pi(r2) {}^{3} = 8 \ratio 27 \\ \\ = > (r1) {}^{3} \ratio (r2) {}^{3} = 8 \ratio 27 \\ \\ = > r1 \ratio r2 = \sqrt[3]{8} \ratio \sqrt[3]{27} \\ \\ = > (r1) \ratio (r2) = 2 \ratio 3$

Now,

Surface areas of the sphere;

$= > 4\pi(r1) {}^{2} \ratio 4\pi(r2) {}^{2} \\ \\ = > (r1) {}^{2} \ratio (r2) {}^{2} = (2) {}^{2} \ratio (3) {}^{2} \\ \\ = > 4 \ratio 9$

Thus,

Ratio of the surface areas of the given spheres is 4:9.

Hope it helps ☺️