Question

which of the following is the correct formula to use solve for h given that the volume of the figure is 500 cubic units?

○ h = \frac { 500 } { 5 ^ { 2 } \pi }

○ h = ( 500 ) ( 2 ) ( 5 ) \pi

○ h = ( 500 ) ( 5 ^ { 2 } ) \pi

○ h = \frac { 500 } { ( 2 ) ( 5 ) \pi }

Explanation:

Step1: Recall the volume formula for a half - cylinder

The volume formula for a full cylinder is \(V=\pi r^{2}h\). For a half - cylinder, the volume formula is \(V = \frac{1}{2}\pi r^{2}h\). Given \(V = 500\) and \(r = 5\).

Step2: Substitute the values into the formula and solve for \(h\)

Substitute \(V = 500\) and \(r = 5\) into \(V=\frac{1}{2}\pi r^{2}h\). We get \(500=\frac{1}{2}\pi(5)^{2}h\).
First, simplify the right - hand side: \(\frac{1}{2}\pi(25)h=\frac{25\pi h}{2}\).
Then, solve for \(h\):

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Answer:

\(h=\frac{500}{5^{2}\pi}\) (the first option)