Question

16. The surface areas of two spheres are in the ratio 16:9. The ratio of their volumes is(a) 64:27
(b) 16:9
(c) 4:3
(d) 16³:9³

Answer 1

Answer:

Option (a)

Step-by-step explanation:

surface area of sphere,A = 4πr²

=> A ∝ r²

=> r ∝ √A

The surface areas of two spheres are in the ratio = 16 : 9

radius of two spheres will be in the ratio =  $\sqrt{\frac{16}{9} } = \frac{4}{3}$

$=> \frac{r1}{r2} = \frac{4}{3}$

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

=> V ∝ r³

$=> \frac{V1}{V2} =(\frac{r1}{r2}) ^{3}\\\\=> \frac{V1}{V2} =(\frac{4}{3}) ^{3}\\\\=> \frac{V1}{V2} = \frac{64}{27}$

VOLUMES ARE IN THE RATIO 64 : 27