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

Vsphere = (4/3) pir^2

remember

d/2=r

original radius is 18/2=9

the new one is 9/2=4.5

solve

new is how much of original?

new/originnal=what?

find each

origiinal = (4/3) pi9^3 = (4/3) pi729

new = (4/3) pi4.5^3 = (4/3) pi91.125

new/originl = ((4/3) pi91.125) / ((4/3) pi729)

the (4/3) pi cancels out

new/original=91.125/729=0.125=1/8

answer is new volume is 1/8 of original

the faster way is

if radius is 1/2 then

(4/3) pi (r/2) ^3

(4/3) pi (r^3/8)

(4/3) pir^3 (1/8)

compared to origninal wihch is

(4/3) pir^3

1/8 of original