Question

the volume of a cone is one - third the volume of a:
a. pyramid
b. cylinder
c. cube
d. sphere

Explanation:

The volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\), and the volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\). When a cone and a cylinder have the same base radius \(r\) and height \(h\), the volume of the cone is one - third of the volume of the cylinder. A pyramid has a different volume formula (\(V = \frac{1}{3}Bh\), where \(B\) is the base area, but it's not in the same geometric family as the cone in terms of this simple one - third relationship with a common - shaped solid like the cylinder). A cube has \(V=a^{3}\) (where \(a\) is the side length) and a sphere has \(V=\frac{4}{3}\pi r^{3}\), neither of which have the one - third relationship with the cone's volume formula in the context of same - base - like and height relationships.

Answer:

B. cylinder