Question

4.There are many cylinders with radius 6 meters. Let h represent the height in meters and Vrepresent the volume in cubic meters.a.Write an equation that represents the volume V as a function of the height h.b.Sketch the graph of the function, using 3.14 as an approximation for π.C.If you double the height of a cylinder, what happens to the volume? Explain this using the equationd.If you multiply the height of a cylinder by 1/3, what happens to the volume? Explain this using the graph.

Answer 1

(a)V=36πh

Step-by-step explanation:

• Radius = 6 meters

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

Part A

An equation that represents the volume V as a function of the height h is:

`\begin{gathered} V=\pi*6^2* h \\ V=36\pi h \end{gathered}`

Part B

Using 3.14 as an approximation for π

`\begin{gathered} V=36*3.14* h \\ V=113.04h \end{gathered}`

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

`V=113.04h`

When h=1

`V=113.04*1=113.04m^3`

If you double the height of a cylinder, h=2:

`V=113.04*2=226.08m^3`

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

`V=113.04h`

If the height of the cylinder is multiplied by 1/3, we have:

`\begin{gathered} V=(113.04h)/(3) \\ V=37.68h \end{gathered}`

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.