Question

what must be known to calculate the volume of a cone?
a. diameter and slant height
b. diameter and height
c. radius and circumference
d. radius and height

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius of the base of the cone and \(h\) is the height of the cone.

Step2: Analyze each option

• Option a: The slant height \(l\) is related to \(r\) and \(h\) by the formula \(l = \sqrt{r^{2}+h^{2}}\). But we cannot directly use slant height in the volume formula \(V=\frac{1}{3}\pi r^{2}h\).
• Option b: If we know the diameter \(d\), we can find the radius \(r=\frac{d}{2}\). But the volume formula requires radius \(r\) (not diameter directly) and height \(h\).
• Option c: If we know the circumference \(C = 2\pi r\), we can find \(r=\frac{C}{2\pi}\). But we still need the height \(h\) for the volume formula.
• Option d: Since \(V=\frac{1}{3}\pi r^{2}h\), if we know the radius \(r\) and height \(h\), we can directly calculate the volume of the cone.

Answer:

d. Radius and height