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

A) The formula for the volume of a sphere in terms of its radius (half the diameter) is
$V= \frac{4}{3}\pi r^{3}$
For your 18 cm sphere, the volume is
$V= \frac{4}{3}\pi(9 cm)^{3} = 972\pi \cdot cm^{3} \approx 3054 cm^{3}$

B) If the diameter were reduced by half, the volume would be $(\frac{1}{2})^{3}=\frac{1}{8}$ of the original volume.

Answer 2

Answer:

Step-by-step explanation:

Volume of sphere$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \left (\frac{d}{2} \right )^3=\frac{1}{6}\pi d^3$

Here diameter, d = 18 cm

Volume of sphere = $=\frac{1}{6}\times \pi \times 18^3=3053.63cm^3$

Let the volume of sphere be V.

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

We have

         $\frac{V}{V'}=\frac{\frac{1}{6}\pi d^3}{\frac{1}{6}\pi \left (\frac{d}{2} \right )^3}=\frac{8}{1}\\\\\frac{V}{V'}=8\\\\V'=\frac{V}{8}$

When diameter were reduced by half the volume becomes $\frac{1}{8}$ times of original volume.