Chapter 12.5, Problem 30SR

To determine

To find: the volume of the trough.

Answer to Problem 30SR

The volume of the tough is $\frac{1}{2}\left(235.5\right){\text{ft}}^3$ that is $117.75{\text{ft}}^3$ .

Explanation of Solution

Given:

  

Formula used:

The volume V of the cylinder is $V=B\cdot h$ .

Calculation:

Consider the figure as shown below:

  

Consider the radius of the tough is 2.5 ft and the height of the tough is 12 ft.

The objective is to find the volume of the tough.

The volume of the tough is half the volume of the full cylinder.

The volume V of the cylinder is $V=B\cdot h$ .

Here, $B=\pi r^2$ is the area of the circle and h is the height the cylinder.

The area B of the circle is,

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(2.5\right)}^2\\ =6.25\pi \\ \approx 6.25\left(3.14\right)\left[\text{Since}\pi \approx 3.14\right]\\ =19.625\end{array}$

Substitute $B\approx 19.625$ and h = 12 in $V=B\cdot h$ .

Thus, the volume V is,

  $\begin{array}{c}V=B\cdot h\\ \approx \left(19.625\right)12\\ =235.5\end{array}$

Thus, the volume of the cylinder is approximately $235.5{\text{ft}}^3$ .

Conclusion:

Therefore, the volume of the tough is $\frac{1}{2}\left(235.5\right){\text{ft}}^3$ that is $117.75{\text{ft}}^3$ .