Chapter 12.3, Problem 20PPS

(a)

To determine

Examine the effect of size of a cylinder on its volume.

Explanation of Solution

Given data:

Radius of cylinder=5 yards

Radius of height of cylinder=3 yards

Formula used:

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

Calculation:

Cylinder	Radius	Height	Volume
Original	5	3	235.5
Multiply radius by 3	15	3	2119.5
Multiply height by 3	5	9	706.5
Multiply both by 3	15	9	6358.5

Conclusion:

The volume of cylinder will increase.

(b)

To determine

Examine the effect of size of a cylinder on its volume.

Answer to Problem 20PPS

When radius multiply by 3: V₁=9V

When height is multiply by 3: V₂=3V

When both multiply by 3: V₃=27V

Explanation of Solution

Given data:

Radius of cylinder=5 yards

Radius of height of cylinder=3 yards

Formula used:

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

Calculation:

Original :

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

When radius multiply by 3:

  $\begin{array}{l}$ {\text{Volume of cylinder(V}}_{\text{1}}\text{)}=\pi {(3\text{r)}}^{\text{2}}h${\text{ V}}_{\text{1}}=9\pi {\text{r}}^{\text{2}}h\\ {\text{ V}}_{\text{1}}=9\text{V}\end{array}$

When height is multiply by 3:

  $\begin{array}{l}{\text{Volume of cylinder(V}}_{\text{2}}\text{)}=\pi {\text{r}}^{\text{2}}3h\\ {\text{ V}}_{\text{2}}=3\pi {\text{r}}^{\text{2}}h\\ {\text{ V}}_{\text{2}}=3\text{V}\end{array}$

When both multiply by 3:

  $\begin{array}{l}$ {\text{Volume of cylinder(V}}_{\text{3}}\text{)}=\pi {(3\text{r)}}^{\text{2}}3h${\text{ V}}_{\text{3}}=27\pi {\text{r}}^{\text{2}}h\\ {\text{ V}}_{\text{3}}=27\text{V}\end{array}$

Conclusion:

When radius multiply by 3: V₁=9V

When height is multiply by 3: V₂=3V

When both multiply by 3: V₃=27V

(c)

To determine

Examine the effect of size of a cylinder on its volume after dilation d.

Answer to Problem 20PPS

  $\text{Volume of cylinder after dilation (d) }=\pi {\text{r}}^{\text{2}}h{d}^3$

Explanation of Solution

Given data:

Radius of cylinder=5 yards

Radius of height of cylinder=3 yards

Formula used:

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

Calculation:

Volume of cylinder after dilation d:

Radius after dilation=rd and height after dilation =dh

  $\begin{array}{l}$ \text{Volume of cylinder after dilation (d)}=\pi {(d\text{r)}}^{\text{2}}dh$=\pi {\text{r}}^{\text{2}}h{d}^3\end{array}$

Conclusion:

  $\text{Volume of cylinder after dilation (d) }=\pi {\text{r}}^{\text{2}}h{d}^3$