Chapter 12.7, Problem 41SPR

To determine

Calculate the volume of the cone.

Answer to Problem 41SPR

The volume of the cone is $0.153m^3$ .

Explanation of Solution

Given:

It is given in the question that the figure is shown below:

  

Concept Used:

In this, use the concept of volume of the cone and the trigonometric ratios.

Calculation:

Since, use the trigonometric ratios,

  

  $\begin{array}{l}\sin {22.5}^{\circ }=\frac{r}{1}\\ r=\sin 22.5\approx 0.3827\end{array}$

Now, the volume of the cone will be:

  $\begin{array}{l}V=\frac{1}{3}\pi r^{2}h\\ $ V=\frac{1}{3}\pi {(0.3827)}^2(1)$V=\frac{1}{3}\pi (0.1464)\\ V=0.153m^3\end{array}$

Conclusion:

The volume is $0.153m^3$ .