Chapter 12.3, Problem 19PPS

To determine

To calculate: Volume of the roll.

Answer to Problem 19PPS

Volume $\left(V\right)$ of the roll is $2991.917c{m}^3$ .

Explanation of Solution

Given:

Length $\left(H\right)$ of the cylinder $=28cm$

Diameter of the large cylinder $=13cm$

Diameter of the small cylinder $=4.5cm$

Radius of the large cylinder $6.5cm$

Rradius of the small cylinder $=2.25cm$

Calculation:

The formula for the volume of roll can be calculated as,

  $V=Bh=\pi r^{2}h$

After putting the values in the equation,

  $V=Vofl\arg ecylinder-V\text{}ofSmall\text{}\text{}Cylinder$

  $V=\pi {\left(r\right)}^2\left(h\right)-\pi {\left(r\right)}^2\left(h\right)$

  $V=\pi {\left(6.2\right)}^2\left(h\right)-\pi {\left(2.1\right)}^2\left(h\right)$

  $\begin{array}{l}V=\pi \left(38.44\right)\left(28\right)-\pi \left(4.41\right)\left(28\right)\\ V=1076.32\pi -123.48\pi \\ V=952.84\pi \\ V=2991.917c{m}^3\end{array}$

Thus, Volume $\left(V\right)$ of the roll is $2991.917c{m}^3$ .