Question

What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?

Answer 1

The volume of the sphere of radius r is:
 V1 = (4/3) * (pi) * (r ^ 3)
 Where,
 r: sphere radius:
 The volume of the sphere of radius 0.3r is:
 V2 = (4/3) * (pi) * ((0.3r) ^ 3)
 Rewriting:
 V2 = (4/3) * (pi) * (0.027 (r) ^ 3)
 V2 = 0.027 (4/3) * (pi) * (r ^ 3)
 V2 = 0.027V1
 The difference is:
 V1-V2 = V1-0.027V1 = V1 (1-0.027)
 V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)
 Answer:
 the difference in volume between a sphere with radius and a sphere with radius 0.3r is:
 V1-V2 = 0.973 * (4/3) * (pi) * (r ^ 3)