Question

the volume of a sphere whose diameter is 18 centimeters is ? cubic centimeters. If its diameter were reduced by half its volume would be ? of its original volume.

Answer 1

Explanation:

Volume of sphere
`=(4)/(3)\pi r^3=(4)/(3)\pi \left ((d)/(2) \right )^3=(1)/(6)\pi d^3`

Here diameter, d = 18 cm

Volume of sphere =
`=(1)/(6)* \pi * 18^3=3053.63cm^3`

Let the volume of sphere be V.

When the diameter reduces to half, the volume be V'.

We have

`(V)/(V')=((1)/(6)\pi d^3)/((1)/(6)\pi \left ((d)/(2) \right )^3)=(8)/(1)\\\\(V)/(V')=8\\\\V'=(V)/(8)`

When diameter were reduced by half the volume becomes
`(1)/(8)` times of original volume.

Answer 2

A) The formula for the volume of a sphere in terms of its radius (half the diameter) is

`V= (4)/(3)\pi r^(3)`
For your 18 cm sphere, the volume is

`V= (4)/(3)\pi(9 cm)^(3) = 972\pi \cdot cm^(3) \approx 3054 cm^(3)`

B) If the diameter were reduced by half, the volume would be
`((1)/(2))^(3)=(1)/(8)` of the original volume.