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