Question

volume of two sphere are in the ratio of 27:64.what is the ratio of their surface areas

Answer 1

Hope this will help u, champ!

Answer 2

Answer:

9:16

Step-by-step explanation:

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

Since we are given that volume of two sphere are in the ratio of 27:64.

⇒$\frac{\frac{4}{3} \pi r^{3}}{\frac{4}{3} \pi R^{3}}=\frac{27}{64}$

⇒$\frac{r^{3}}{R^{3}}=\frac{27}{64}$

⇒$\frac{r}{R}=\sqrt[3]{\frac{27}{64}}$

⇒$\frac{r}{R}=\frac{3}{4}$

Thus the ratio of the radii is 3:4

Let the ratio be x

So radii are 3x and 4x

Surface area of sphere = $4\pi x^{2}$

Surface area of sphere of radius 3x= $4\pi (3x)^{2}$

                                                          = $36\pi x^{2}$

Surface area of sphere of radius 4x= $4\pi (4x)^{2}$

                                                          = $64\pi x^{2}$

Ratio of their surface area = $\frac{36\pi x^{2}}{64\pi x^{2}}$

                                           = $\frac{36}{64}$

                                           = $\frac{9}{16}$

Hence the ratio of their surface area is 9:16