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?

πx²
2πx³
\frac{1}{3}πx²
\frac{1}{12}πx³

Explanation:

Step1: Find the radius of the cone

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

Step2: Recall the volume formula for a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\).

Step3: 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)