Question

1. which shape has a volume formula that includes a factor of $\frac{1}{3}$?

a. sphere
b. cone
c. cylinder
d. cube

Explanation:

• Sphere: The volume formula is \(V = \frac{4}{3}\pi r^{3}\), which has a \(\frac{4}{3}\) factor, not \(\frac{1}{3}\).
• Cone: The volume formula is \(V=\frac{1}{3}\pi r^{2}h\), which includes a factor of \(\frac{1}{3}\).
• Cylinder: The volume formula is \(V = \pi r^{2}h\), with no \(\frac{1}{3}\) factor.
• Cube: The volume formula is \(V = s^{3}\) (where \(s\) is the side - length), with no \(\frac{1}{3}\) factor.

Answer:

B. Cone