Question

The ratio of radii of two spheres 2:3find the ratio of their surface area and volumes

Answer 1

S(1)/S(2) = 4πr^2/4πR^2 = 4/9

V(1)/V(2) = 4/3 πr^3 / 4/3 πR^3 = 8/27

Answer 2

Answer:

The ratio of their surface area is 4:9

The ratio of their volume is 8:27

Step-by-step explanation:

The ratio of radii of two spheres 2:3

let the ratio be x

So, radii area 2x and 3x

Surface area of sphere = 4πr^2

So, the ratio of their surface area = [4π(2x)^2]/[4π(3x)^2]

                                                       = [4x^2]/[9x^2]

                                                       = 4/9

Thus the ratio of their surface area is 4:9

Volume of sphere = (4/3) π r^3

So, the ratio of their volume = [(4/3) π (2x)^3]/[(4/3) π (3x)^3]

                                                       = [8x^3]/[27x^3]

                                                       = 8/27

Thus the ratio of their volume is 8:27