Question

the volume of 2spheres are in ratio 64:21.find ratio their surface area

please it's urgent

Answer 1

Let , the radius of first and second sphere is x and y respectively.

As we know that : Volume of sphere :

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


Now, according to the question :

$\frac{ \frac{4}{3}\pi {x}^{3} }{ \frac{4}{3}\pi {y}^{3} } = \frac{64}{27} \\ \\ = > {( \frac{x}{y}) }^{3} = {( \frac{4}{3}) }^{3} \\ \\ = > \frac{x}{y} = \frac{4}{3}$

So, the radius of first and second sphere are 4 and 3 respectively.

As we know that : Surface area of sphere

$4\pi {r}^{2}$

Now, according to the question :

$\frac{4\pi {(4)}^{2} }{4\pi {(3)}^{2} } \\ \\ = > \frac{16}{9}$

So, the Ratio of their surface area will be 16:9