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Activity Discussion Math Volume of Sphere

• # Volume of Sphere

Posted by on June 23, 2023 at 7:00 pm

A solid sphere and a hollow sphere have the same outer radius. The solid sphere has a volume of 36π cubic units, while the hollow sphere has a volume of 16π cubic units. What is the ratio of the inner radius of the hollow sphere to the outer radius?

replied 3 months ago 2 Members · 1 Reply
• ### Bikesh

Member
June 23, 2023 at 8:26 pm
0

Given

→The outer radius of solid sphere and hollow sphere are same

→So we Consider outer Radius of solid sphere and hollow sphere is R

→Volume of solid sphere = 36π cubic unit

→Volume of hollow sphere = 16π cubic unit

To Find

Assume

→Inner radius of hollow sphere = r

Formula

→Volume of Solid Sphere = 4/3πR³

→Volume of Hollow Sphere = 4/3πR³ – 4/3πr³

Now Take

Volume of solid sphere = 36π cubic unit

→ 4/3πR³ = 36π

Volume of hollow sphere = 16π cubic unit

→ 4/3πR³ – 4/3πr³ = 16π

→36π – 4/3πr³ = 16π

→36π – 16π = 4/3πr³

→20π = 4/3πr³

→5×3 = r³

→r³ = 15

Now Take Volume of solid sphere

4/3πR³ = 36π

→R³ = 27

According to question

→r³/R³ = 15/27

→r/R = ³√(15/27)