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If a cylinder has a height of 7 inches and avolume of 2,908.33 ins, find its diameter.

Sagot :

Remember that the formula for the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

We know that:

[tex]r=\frac{D}{2}[/tex]

Thereby,

[tex]V=\pi r^2h\rightarrow V=\pi(\frac{D}{2})^2h\rightarrow V=\frac{\pi D^2h}{4}[/tex]

Solving for D,

[tex]\begin{gathered} V=\frac{\pi D^2h}{4}\rightarrow4V=\pi D^2h\rightarrow\frac{4V}{\pi h}=D^2 \\ \rightarrow D=\sqrt[]{\frac{4V}{\pi h}} \end{gathered}[/tex]

Using the data given,

[tex]\begin{gathered} D=\sqrt[]{\frac{4V}{\pi h}} \\ \\ \Rightarrow D=23 \end{gathered}[/tex]

We get that the diameter of the cylinder is 23"

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