Question

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

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

Explanation:

Step1: Recall volume formulas

• Cone: \( V=\frac{1}{3}\pi r^{2}h\) (has a factor of \(\frac{1}{3}\)).
• Cylinder: \( V = \pi r^{2}h\) (no factor of \(\frac{1}{3}\)).
• Sphere: \( V=\frac{4}{3}\pi r^{3}\) (has a factor of \(\frac{4}{3}\), not \(\frac{1}{3}\)).
• Cube: \( V = s^{3}\) (no factor of \(\frac{1}{3}\)).

Answer:

a. Cone