Question

1. to find the volume of a cone, you need to know:

a. the circumference and the height
b. the radius of the base and the height
c. the diameter and the height
d. the slant height and the radius

Explanation:

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height. So, to use this formula, we need to know the radius of the base and the height.

• Option a: The circumference \(C = 2\pi r\), we can find \(r=\frac{C}{2\pi}\) from the circumference. But having the circumference and height is an extra - step (since we can directly use radius).
• Option c: If we know the diameter \(d\), we can find \(r=\frac{d}{2}\). But again, using diameter is an extra - step compared to using radius directly.
• Option d: The slant height \(l\) is related to \(r\) and \(h\) by the formula \(l=\sqrt{r^{2}+h^{2}}\). We still need to know either \(h\) (if we know \(r\) and \(l\)) or \(r\) (if we know \(h\) and \(l\)) to calculate the volume using the formula \(V = \frac{1}{3}\pi r^{2}h\).

Answer:

B. the radius of the base and the height