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.

• Option a: The circumference \(C = 2\pi r\) can be used to find \(r\) (\(r=\frac{C}{2\pi}\)), but it is an extra - step. The direct requirement is \(r\) (not circumference) and \(h\).
• Option b: Since \(V=\frac{1}{3}\pi r^{2}h\), knowing \(r\) (radius of the base) and \(h\) (height) is sufficient.
• Option c: The diameter \(d = 2r\) can be used to find \(r\) (\(r=\frac{d}{2}\)), but it is an extra - step. The direct requirement is \(r\) (not diameter) and \(h\).
• Option d: The slant height \(l\) is related to \(r\) and \(h\) by the formula \(l=\sqrt{r^{2}+h^{2}}\). But the volume formula does not use \(l\) directly; it uses \(r\) and \(h\).

Answer:

B. the radius of the base and the height