Chapter 12.6, Problem 3PSA

To determine

To find: The volume of the grain silo with height 15 m and radius 3 m.

Answer to Problem 3PSA

The volume of the grain silo is $481{\text{m}}^3.$

Explanation of Solution

Given Information:

Radius of a cylinder $\left(r\right)=3\text{m}$

Height of a cylinder $\left(h\right)=15\text{m}$

Radius of a hemisphere $\left(r_1\right)=r=3\text{m}$

Formula used:

Volume of a cylinder $\left(V\right)=\pi r^{2}h$

  $r\text{and}h$ are the radius and height of a cylinder

Volume of a hemisphere $\left(V_1\right)=\frac{2}{3}\pi r_1{}^3$

  $r_1$ is the radius of a hemisphere

Calculation:

The grain silo is formed by placing hemisphere on a cylinder.

So, Volume of the grain silo $\left(V\text{'}\right)=$ Volume of cylinder + Volume of hemisphere

We know that,

Volume of a cylinder $\left(V\right)=\pi r^{2}h$

Volume of a hemisphere $\left(V_1\right)=\frac{2}{3}\pi r_1{}^3$

  $\therefore V\text{'}=V+V_1$

As $r=3\text{m},h=15\text{m},r_1=3\text{m}$

  $\begin{array}{l}\therefore V\text{'}=\left(\frac{22}{7}\times 3^2\times 15\right)+\left(\frac{2}{3}\times \frac{22}{7}\times 3^3\right)\\ \therefore V\text{'}=424.28+56.57\\ \therefore V\text{'}=480.85{\text{m}}^3\approx 481{\text{m}}^3\end{array}$

Hence, the volume of grain silo is $481{\text{m}}^3.$