Question

A bar of platinum has a length of 49.7 millimeters, and a height of 3.4 millimeters. Describe how multiplying the length by 1/3 affects the volume.

Answer 1

The volume of a rectangular bar is given by the formula:

$V=h\times l^2$

Where l is the length and h is the height. if we multiply the height of the bar by 1/3, we get:

$hnew=\frac{1}{3}h$

By replacing this new height in the formula of the volume of the bar, we get:

$Vnew=\frac{1}{3}h\times l^2$

As we can see, when we multiply the height by 1/3 the same happens with the Volume, this means that the volume of the second bar (after taking 1/3 of its height) is one-third the volume of the first bar. Then the volume of the bar decreases.