Question

the ratio of radii of two sphers is 2:3.Find the ratio of their surface area and volumes​

Answer 1

Answer:

Ratio of surface area= 4/9

Ratio of volume = 8/27

Step-by-step explanation:

$area \: is \: directly \: proportional \: to \: {r}^{2} \\ so \: ratio \: of \: area = { (\frac{2}{3} })^{2} = \frac{4}{9} \\ ratio \: of \: volume \: directly \: proportional \: to \: {r}^{3} = { (\frac{2}{3} })^{3} \\ \frac{8}{27}$

Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\orange{Given:}$

Ratio of radii of two spheres is 2:3

$\bold\pink{To \ find:}$

Ratio of their surface area and volumes

$\bold\green{\underline{\underline{Solution}}}$

Let radii of one of the sphere be 2 units and of the other be 3 units.

(1)Ratio of their surface area

$surface \: area \: of \: sphere = \\ 4\pi \: {r}^{2}$

Surface area of first sphere=$\bold{4× \pi×2^{2}}$

=${\pi×16}$

Surface area of second sphere=$\bold{4×\pi×3^{2}}$

=${\pi×36}$

Ratio of their surface areas=$\bold{\frac{\pi×16}{\pi×32}}$

=${\frac{4}{9}}$

=${4:9}$

(2)Ratio of their volumes

$volume \: of \: sphere = \\ \frac{4}{3} \times \pi \times {r}^{3}$

$\bold{Volume \ of \ first \ sphere =\frac{4}{3}×\pi×2^{3}}$

$\bold{=\frac{4}{3}×\pi×8}$

$\bold{Volume \ of \ second \ sphere =\frac{4}{3}×\pi×3^{3}}$

$\bold{=\frac{4}{3}×\pi×27}$

Ratio of their volumes=$\bold{\frac{\frac{4}{3}×\pi×8}{\frac{4}{3}×\pi×27}}$

=$\bold{\frac{8}{27}}$

=$\bold{8:27}$

Therefore,

$\bold\purple{Ratio \ of \ their \ surface \ areas \ is \ 4:9}$

$\bold\purple{Ratio \ of \ their \ volumes \ is \ 8:27}$