Question

Two spheres have their surface area in the ratio 9:16.Their volumes are in the ratio of ___

Answer 1

27:64

Let the radii be r and R

Given: 4πr/4πR = 9/16 (ratio of surface areas)
So, r/R = 3/4

Ratio of volume = (4/3)πr³/(4/3)πR³ = r³/R³ = 27/64

Answer 2

Dear Student,

◆ Answer -

V1/V2 = 27/64

● Explanation -

Let r1 and r2 be radii of circle.

Surface area of two spheres is given by -

A1/A2 = (4πr1^2) / (4πr2^2)

9/16 = (r1/r2)^2

r1/r2 = 3/4

Volumes of two spheres are in the ratio is -

V1/V2 = (4/3 πr1^3) / (4/3 πr2^3)

V1/V2 = (r1/r2)^3

V1/V2 = (3/4)^3

V1/V2 = 27/64

Hence, volumes of two spheres are in the ratio of 27:64.

Thanks dear. Hope this helps you...