Question

the base diameter and the height of a cone are both equal to x units. which expression represents the volume of the cone, in cubic units? \\(\circ\\) \\(\pi x^2\\) \\(\circ\\) \\(2\pi x^3\\) \\(\circ\\) \\(\frac{1}{3}\pi x^2\\) \\(\circ\\) \\(\frac{1}{12}\pi x^3\\)

Explanation:

Step1: Find the radius of the cone

The diameter \(d = x\), and the radius \(r=\frac{d}{2}=\frac{x}{2}\).

Step2: Use the volume formula for a cone

The volume formula for a cone is \(V = \frac{1}{3}\pi r^{2}h\). Substitute \(r=\frac{x}{2}\) and \(h = x\) into the formula:

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Answer:

\(\frac{1}{12}\pi x^{3}\) (the fourth option)