Chapter 12.5, Problem 22PPS

To determine

To determine the volume of the right cone.

Answer to Problem 22PPS

  $V=5.8{\text{ centimeter}}^3$

Explanation of Solution

Given:

Slant height $=5.6$ centimeter

Radius $=1$ centimeter

Formula used:

Volume of the cone, $V=\frac{1}{3}\pi r^{2}h$

Slant height, $l=\sqrt{{\text{radius}}^2+{\text{height}}^2}$

Calculation:

Slant height $=5.6$ centimeter

Radius $=1$ centimeter

Slant height can be represented as $l$ , height is $h$ and radius $r$ .

  $\Rightarrow l=\sqrt{r^2+h^2}$

  $\Rightarrow h=\sqrt{l^2-r^2}$

  $\Rightarrow h=\sqrt{{(5.6)}^2-{(1)}^2}$

  $\Rightarrow h=\sqrt{30.36}$

  $\Rightarrow h=5.5099$ Centimeter

Now,

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(1)}^2\times 5.5099$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 17.309$

  $\Rightarrow$ Volume of the cone $V=5.769{\text{ centimeter}}^3$

The value of the volume of the cone nearest to tenth is $V=5.8{\text{ centimeter}}^3$ .

Conclusion:

Therefore, the volume of the right cone is $V=5.8{\text{ centimeter}}^3$ .