Chapter 12.5, Problem 38HP

To determine

To determine the volume of cylinder that has same radius and height as the cone.

Answer to Problem 38HP

  $1703.999{\text{ centimeter}}^3$

Explanation of Solution

Given:

Volume of the cone $=568{\text{ centimeter}}^3$

Formula used:

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

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Volume of cylinder $=\pi r^{2}h\left[r\text{=}\text{radius, }h\text{=}\text{height}\right]$

Calculation:

Given, volume of the cone $=568{\text{ centimeter}}^3.$

So at first the expression of the radius and height need to be expressed.

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

Volume of the cone $=568{\text{ centimeter}}^3$

So,

  $\Rightarrow \frac{1}{3}\pi r^{2}h=568$

  $\Rightarrow r^{2}h=\frac{568\times 3}{\pi }$

  $\Rightarrow r^{2}h=\frac{1704}{\pi }$

  $\Rightarrow r^{2}h=542.4$

This is the expression of radius and height,

Now,

Volume of cylinder $=\pi r^2\text{h }$

Here, putting $r^{2}h=542.4$ in the expression of volume of cylinder

  $\Rightarrow$ Volume of cylinder $=\pi \times 542.4$

  $\Rightarrow$ Volume of cylinder $=\pi \times 542.4$

  $\Rightarrow$ Volume of cylinder $=1703.999{\text{ centimeter}}^3$

Conclusion:

Therefore, the volume of cylinder that has same radius and height as the cone is $=1703.999{\text{ centimeter}}^3$ .