Question

an oblique cylinder has a diameter of 14 units. the volume of the cylinder is 1,176π cubic units. what is x, the height of the cylinder? 21 units 24 units 25 units 28 units

Explanation:

Step1: Calculate the radius

The diameter \(d = 14\) units, so the radius \(r=\frac{d}{2}=\frac{14}{2}=7\) units.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). We know \(V = 1176\pi\) and \(r = 7\). Substitute these values into the formula:
\(1176\pi=\pi\times(7)^{2}\times x\)
First, simplify \(\pi\times(7)^{2}\times x=\pi\times49\times x = 49\pi x\).
So the equation becomes \(1176\pi=49\pi x\).
Divide both sides by \(49\pi\): \(x=\frac{1176\pi}{49\pi}\).
Since \(\frac{\pi}{\pi}=1\), then \(x=\frac{1176}{49}=24\).

Answer:

24 units