Question

the volume of a sphere whose diameter is 18 centimeters is 246 324 648 972 π cubic centimeters. if its diameter were reduced by half, its volume would be 1/2 1/4 1/6 1/8 of its original volume.

Answer 1

radius of sphere = 18/2 = 9 cm

Volume of sphere = 4/3 πr^3 = 4/3 x π x (9)^3 = 972 π cubic cm

If the diameter is reduced by half, then
Volume = 4/3 x π x (9/2)^3 = 4/3 x π x (9)^3 x (1/2)^3 = 1/8(972)

Therefore, new volume is 1/8 of original volume.

Answer 2

The volume of the sphere would be 1/8 of the original volume

How to determine the changes when the diameter is halved?

The volume of a sphere is:

V= π(d/2)³

When the diameter is halved, we have:

V2= π(d/2/2)³

This gives

V2= 1/8 * π(d/2)³

Substitute V= π(d/2)³

V2= 1/8V

Hence, the volume of the sphere would be 1/8 of the original volume

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