A large sphere has the radius of 6 centimeters. A small sphere is inside the sphere. After the volume of the small sphere is sub

Question

2 years ago

11

tracted, the volume left in the large sphere is 252pi cubic inches what is the radius of the small sphere

1 answer:

neonofarm [45] · Answer 1 · 2022-03-31T18:07:25+03:00

Answer:

3 in

Step-by-step explanation:

The volume of the large sphere is ...

V = (4/3)πr³ = 288π . . . cubic inches

The volume of the smaller sphere is ...

288π -252π = 36π . . . cubic inches

The ratio of volumes of the smaller sphere to the larger is the cube of the ratio of radii. The radius of the smaller sphere will be ...

(6 in)∛(36π/(288π)) = (6 in)∛(1/8) = 3 in . . . . small sphere radius