Chapter 12.5, Problem 37HP

To determine

To determine the correct step of calculation of the volume.

Answer to Problem 37HP

Cornelio is correct

Explanation of Solution

Given:

  

  

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:

Given figure,

  

Slant height of cone $=13\text{ centimeter}$

Radius of cone $=5\text{ centimeter}$

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

  $\Rightarrow l=\sqrt{r^2+h^2}$

  $\Rightarrow h=\sqrt{l^2-r^2}$

  $\Rightarrow h=\sqrt{{(13)}^2-{(5)}^2}$

  $\Rightarrow h=\sqrt{144}$

  $\Rightarrow h=12$ Centimeter

Now volume of the cone,

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

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(5)}^2\times 12$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 942.477$

  $\Rightarrow$ Volume of the cone $V=314.159{\text{ centimeter}}^3$

This can be written as,

  $V\approx 314.2{\text{ centimeter}}^3$

This is the correct format of solving the following problem and Cornelio is correct

  

But Alexander did it in a wrong way as the height given here is slant height of the cone not the normal height. So, for that at first one need to find the height then one can find the volume of the cone. So, Cornelio is correct

Conclusion:

Therefore, the correct step of calculation of the volume is done by Cornelio.