Question

the surface area of the two sphere are in the ratio 49:16 the ratio of their volume is
a 4:3
b 7:4
c 7:3
d 3: 4
please give step by step explanation ​

Answer 1

Answer:

343/64

Step-by-step explanation:

formula for the surface area of the sphere is 4πr^2

let the radius of the spheres be R and r and surface area be A and a, volume be V and v.

since,

A/a = 49/16.

4πR^2/4πr^2 = 49/16

(by cancellations)

R^2/r^2 = 49/16

taking square root on both sides

R/r = 7/4.---------

Now ratio of volumes is

(4/3 πR^3)/(4/3 πr^3)

which is (by cancellations)

R^3/r^3=(R/r)^3=(7/4)^3=343/64

So I would rather say that there's no correct option.