Question

A sphere of radius r has surface area

A = 4r2and volume V = (4/3r^3) The radius of sphere 2 is triple the radius of sphere 1.

(a)
What is the ratio of the areas, A2/A1?

(b)
What is the ratio of the volumes, V2/V1?

Answer 1

A2/A1 = 9

V2/V1 = 27

Step-by-step explanation:

Area of Sphere 1; A1 = 4πr²

Volume of Sphere 1; V1 = (4/3)πr³

Area of Sphere 2; A2 = 4π(3r)² = 9*4πr²

Volume of Sphere 2; V2 = (4/3)π(3r)³ = 27*(4/3)πr³

Thus;

A2/A1 = 9*4πr²/4πr² = 9

V2/V1 = [27*(4/3)πr³]/[(4/3)πr³] = 27