Answer:
(a)V=36πh
Explanation:
• Radius = 6 meters
[tex]\text{Volume of a cylinder}=\pi r^2h[/tex]Part A
An equation that represents the volume V as a function of the height h is:
[tex]\begin{gathered} V=\pi\times6^2\times h \\ V=36\pi h \end{gathered}[/tex]Part B
Using 3.14 as an approximation for π
[tex]\begin{gathered} V=36\times3.14\times h \\ V=113.04h \end{gathered}[/tex]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:
[tex]V=113.04h[/tex]When h=1
[tex]V=113.04\times1=113.04m^3[/tex]If you double the height of a cylinder, h=2:
[tex]V=113.04\times2=226.08m^3[/tex]We observe that when the height is doubled, the volume of the cylinder is also doubled.
Part D
The initial equation for volume is:
[tex]V=113.04h[/tex]If the height of the cylinder is multiplied by 1/3, we have:
[tex]\begin{gathered} V=\frac{113.04h}{3} \\ V=37.68h \end{gathered}[/tex]The volume of the cylinder will be divided by 3.
Using the graph, we observe a horizontal stretch of the graph by 1/3.
