Chapter 12.3, Problem 25HP

a.

To determine

Ratio of volume of cylinder $A$ to cylinder $B$ .

Answer to Problem 25HP

Ratio of volume of cylinder $A$ to cylinder $B$ for the given condition is $2$ .

Explanation of Solution

Given:

Condition: cylinder $A$ has the same radius but twice the height of cylinder $B$ .

Concept Used:

Volume of cylinder is calculated by,

  $V=\pi {\left(r\right)}^2\left(h\right)$

Where,

  $V=$ volume of cylinder.

  $r=$ radius of cylinder.

  $h=$ height of cylinder.

Calculation:

Let,

For cylinder $A:$

Radius $:r$

Height $:2h$ cylinder $B$ .

For cylinder $B:$

Radius $:r$

Height $:h$

Volume of cylinder for given condition is calculated by,

  $V=\pi {\left(r\right)}^2\left(h\right)$

Ratio of volume of cylinder $A$ to cylinder $B$ .

  $\begin{array}{l}\frac{VolofA}{VolofB}=\frac{\pi {\left(r\right)}^2\left(2h\right)}{\pi {\left(R\right)}^2\left(h\right)}\\ =\frac{\pi {\left(R\right)}^2\left(2h\right)}{\pi {\left(R\right)}^2\left(h\right)}\\ =\frac{\pi R^2\left(2h\right)}{\pi R^2\left(h\right)}\\ =\frac{\left(2h\right)}{\left(h\right)}=2\end{array}$

Conclusion:

Thus, Ratio of volume of cylinder $A$ to cylinder $B$ for the given condition is $2$ .

b.

To determine

Ratio of volume of cylinder $A$ to cylinder $B$ .

Answer to Problem 25HP

Ratio of volume of cylinder $A$ to cylinder $B$ for the given condition is $4$ .

Explanation of Solution

Given:

Condition: cylinder $A$ has the same height but twice the radius of cylinder $B$ .

Concept Used:

Volume of cylinder is calculated by,

  $V=\pi {\left(r\right)}^2\left(h\right)$

Where,

  $V=$ volume of cylinder.

  $r=$ radius of cylinder.

  $h=$ height of cylinder.

Calculation:

Let,

For cylinder $A:$

Radius $:2r$ cylinder $B$ .

Height $:h$

For cylinder $B:$

Radius $:r$ cylinder $B$ .

Height $:h$

Volume of cylinder for given condition is calculated by,

  $V=\pi {\left(r\right)}^2\left(h\right)$

Ratio of volume of cylinder $A$ to cylinder $B$ .

  $\begin{array}{l}\frac{VolofA}{VolofB}=\frac{\pi {\left(2R\right)}^2\left(h\right)}{\pi {\left(R\right)}^2\left(h\right)}\\ =\frac{\pi 4R^2\left(h\right)}{\pi {\left(R\right)}^2\left(h\right)}\\ =\frac{\pi 4R^2\left(h\right)}{\pi {\left(R\right)}^2\left(h\right)}\\ =4\end{array}$

Conclusion:

Thus, Ratio of volume of cylinder $A$ to cylinder $B$ for the given condition is $4$ .