Chapter 12.6, Problem 25HP

a)

To determine

To find : Volume of cylinder ration.

Answer to Problem 25HP

  $2:1$

Explanation of Solution

Given Information :

We know that

Radius of cylinder B = R, Radius of cylinder A = r,

Height of cylinder B = H, Radius of cylinder A = h

Formula Used:

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

Calculation :

Ratio of volume of cylinder A to cylinder B

  $\begin{array}{l}=\frac{\pi r^{2}h}{\pi R^{2}H}\left\{H=\frac{1}{2}h,r=R\right\}\\ =\frac{2H}{H}\\ =2:1\end{array}$

b)

To determine

To find : Ratio of volume of cylinder A to B.

Answer to Problem 25HP

  $4:1$

Explanation of Solution

Given Information :

Radius of cylinder A = r = 2R

Height of cylinder A = h = H

Formula Used:

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

Calculation :

Ratio of volume of cylinder A to cylinder B

  $\begin{array}{l}=\frac{\pi {(2R)}^{2}h}{\pi R^{2}h}\\ =\frac{4}{1}\end{array}$

Hence, ratio of volume of cylinder A to cylinder B = $4:1$ .