Chapter 12.4, Problem 35PPS

To determine

To find:

The difference in volume between the largest and smallest possible column.

Answer to Problem 35PPS

The difference between the largest and smallest possible column is ${\text{3190680 cm}}^3$ .

Explanation of Solution

Given information:

The diameter of the column can be between $30$ centimeters and $95$ centimeters. The height is to be $500$ centimeters.

Calculation:

The diameter of the largest possible column is $95$ centimeters.

The radius of the largest possible column is $\frac{95}{2}=47.5$ centimeters.

The diameter of the smallest possible column is $30$ centimeters.

The radius of the smallest possible column is $\frac{30}{2}=15$ centimeters.

The difference between the volumes is:

  $\begin{array}{c}V=V_1-V_2\\ =\pi {\left(47.5\right)}^2\cdot 500-\pi {\left(15\right)}^2\cdot 500\\ =1128125\pi -112500\pi \\ =1015625\pi \\ \approx 3190680\end{array}$

Hence the difference between the largest and smallest possible column is ${\text{3190680 cm}}^3$ .