Question

what happens to the volume of a sphere if its radius is halved?
a. the volume is halved.
b. the volume stays the same.
c. the volume is reduced to one - fourth.
d. the volume is reduced to one - eighth.

the volume of a sphere is measured in what units?
a. linear units
b. square units
c. cubic units
d. spherical units

Explanation:

First Question

Step1: Recall the volume formula of a sphere

The volume formula of a sphere is \(V = \frac{4}{3}\pi r^{3}\).

Step2: Substitute \(r=\frac{r}{2}\) into the formula

When \(r\) is replaced with \(\frac{r}{2}\), the new volume \(V'=\frac{4}{3}\pi(\frac{r}{2})^{3}=\frac{4}{3}\pi\frac{r^{3}}{8}=\frac{1}{8}V\).

Second Question

Step1: Understand the nature of volume units

Volume measures the amount of space occupied by a 3 - dimensional object. Linear units (\(m\), \(cm\) etc.) measure length, square units (\(m^{2}\), \(cm^{2}\) etc.) measure area. Cubic units (\(m^{3}\), \(cm^{3}\) etc.) are used for volume as volume is a 3 - dimensional quantity.

Answer:

1. d. The volume is reduced to one - eighth.
2. c. Cubic Units.