Question

the ratio of radii of two spheres is 1 ratio 3 what is the ratio of their volumes and what is the ratio of their surface areas

Answer 1

Answer ->

Let radius of one sphere be R

Radius of second sphere be r

R/r = 1/3 (given).

Volume of sphere = 4/3π r^3.

Volume of sphere with radius R = 4/3 π R^3.

Volume of sphere with radius r = 4/3πr^3.

Ratio of volume = 4/3 π R^3 / 4/3π r^3

= R^3 / r^3

= 1^3 / 3^3

= 1/27

Total surface area of sphere with radius R = 4πR^2

TSA of sphere with radius r = 4πr^2

Ratio = 4πR^2 / 4πr^2

= R^2/r^2

= 1^2 / 3^2

= 1/9.

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