Question

how is the volume of a cone calculated?
volume = \frac{1}{3} \times \pi \times r^{2} \times h
volume = \frac{1}{4} \times base area \times height
volume = \pi \times radius \times height
volume = \frac{1}{2} \times base area \times height

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a cone is given by \( V=\frac{1}{3}\times\pi\times r^{2}\times h \), where \( r \) is the radius of the base and \( h \) is the height. Also, since the base area \( A = \pi r^{2} \), the formula can be written as \( V=\frac{1}{3}\times A\times h \).

Step2: Analyze each option

• Option a: \( V=\frac{1}{3}\times\pi\times r^{2}\times h \) is the correct formula.
• Option b: The coefficient should be \( \frac{1}{3} \), not \( \frac{1}{4} \).
• Option c: The formula \( V=\pi\times r\times h \) is incorrect. The correct formula has \( r^{2} \) and a factor of \( \frac{1}{3} \).
• Option d: The coefficient should be \( \frac{1}{3} \), not \( \frac{1}{2} \).

Answer:

A. Volume \(=\frac{1}{3}\times\pi\times r^{2}\times h\)