Question

which equation represents the volume of a cone with the same base and height as the cylinder below?

\\(v_{\text{cone}} = \pi t^2 k\\)

\\(v_{\text{cone}} = \frac{1}{3} \pi t^2 k\\)

\\(v_{\text{cone}} = \frac{1}{2} \pi t^2 k\\)

\\(v_{\text{cone}} = 3 \pi t^2 k\\)

Explanation:

Identify the dimensions of the cylinder

The cylinder has a radius of \(t\) and a height of \(k\).

Apply the volume formula for a cone

The volume of a cone with radius \(r\) and height \(h\) is given by:

$$V_{\text{cone}} = \frac{1}{3}\pi r^2 h$$

Substitute the given dimensions

Substituting \(r = t\) and \(h = k\) into the formula:

$$V_{\text{cone}} = \frac{1}{3}\pi t^2 k$$

Answer:

• (A) \(V_{\text{cone}} = \pi t^2 k\)
• (B) \(V_{\text{cone}} = \frac{1}{3}\pi t^2 k\) (Correct answer)
• (C) \(V_{\text{cone}} = \frac{1}{2}\pi t^2 k\)
• (D) \(V_{\text{cone}} = 3\pi t^2 k\)