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

1/4, since the radius is also halved if the diameter is halved, meaning (radius/2)^2 is radius^2 * 1/4.

Answer 2

Answer with Step-by-step explanation:

Volume of sphere is given by

V=
`(4)/(3)\pi r^3`

where r is the radius of sphere

Let d be the diameter then, r=d/2

d=18 cm

⇒ r=9 cm

V=
`(4)/(3)\pi 9^3`

V=
`(4)/(3)\pi * 9^3`

V=972π cubic centimeters

When diameter is reduced to half

⇒radius is reduced to half

⇒ r'=r/2

⇒V'=
`(4)/(3)\pi r'^3`

⇒ V'=
`(4)/(3)\pi (r^3)/(2^3)`

⇒ V'=V/8

Hence, If its diameter were reduced by half, its volume would be 1/8 of its original volume.