Answer with Step-by-step explanation:
Volume of sphere is given by
V=[tex]\dfrac{4}{3}\pi r^3[/tex]
where r is the radius of sphere
Let d be the diameter then, r=d/2
d=18 cm
⇒ r=9 cm
V=[tex]\dfrac{4}{3}\pi 9^3[/tex]
V=[tex]\dfrac{4}{3}\pi \times 9^3[/tex]
V=972π cubic centimeters
When diameter is reduced to half
⇒radius is reduced to half
⇒ r'=r/2
⇒V'=[tex]\dfrac{4}{3}\pi r'^3[/tex]
⇒ V'=[tex]\dfrac{4}{3}\pi \dfrac{r^3}{2^3}[/tex]
⇒ V'=V/8
Hence, If its diameter were reduced by half, its volume would be 1/8 of its original volume.
