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

Answer with Step-by-step explanation:

Volume of sphere is given by

V=$\dfrac{4}{3}\pi r^3$

where r is the radius of sphere

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

d=18 cm

⇒ r=9 cm

V=$\dfrac{4}{3}\pi 9^3$

V=$\dfrac{4}{3}\pi \times 9^3$

V=972π cubic centimeters

When diameter is reduced to half

⇒radius is reduced to half

⇒ r'=r/2

⇒V'=$\dfrac{4}{3}\pi r'^3$

⇒ V'=$\dfrac{4}{3}\pi \dfrac{r^3}{2^3}$

⇒ V'=V/8

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

Answer 2

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