Chapter 12.8, Problem 1ACYP

To determine

To compare the given cylinders and find their volume.

Answer to Problem 1ACYP

  $261.392\pi$ cubic meter

Explanation of Solution

Given:

Two cylinders.

  

Concept used:

Two solids are similar if they are the same type of solid and their corresponding radii and heights are proportional.

Formula used:

Volume of a cylinder, $V=\pi r^{2}h$

Calculation:

For the given two cylinders,

Match up the corresponding radii and heights.

  $\frac{\text{First cylinder}}{\text{Second cylinder}}=\frac{6.2}{6.2}=\frac{6.8}{6.8}=\frac{1}{1}$

Here, the result is a number. It means that they are proportional.

So, congruent ratios show that the given two cylinders are similar.

Volume of first cylinder, $V=\pi r^{2}h$

  $\begin{array}{l}=\pi \times {\left(6.2\right)}^2\times 6.8\\ =\pi \times 38.44\times 6.8\\ =261.392\pi \end{array}$

Volume of second cylinder, $V=\pi r^{2}h$

  $\begin{array}{l}=\pi \times {\left(6.2\right)}^2\times 6.8\\ =\pi \times 38.44\times 6.8\\ =261.392\pi \end{array}$

Conclusion:

Therefore, the given two cylinders are similar and their volume is $261.392\pi$ cubic meter.