Question

which of the following formulas is used to calculate the area of the base of a cone?
a. $\frac{4}{3}pi r^{3}$
b. $pi r^{2}$
c. $\frac{1}{3}pi r^{2}$
d. $pi r^{2}h$

Explanation:

Step1: Analyze the base of a cone

The base of a cone is a circle.

Step2: Recall the area formula of a circle

The area formula of a circle is $A = \pi r^{2}$, where $r$ is the radius of the circle.

Step3: Check each option

• Option a: $\frac{4}{3}\pi r^{3}$ is the volume formula of a sphere.
• Option b: $\pi r^{2}$ is the area formula of a circle (base of a cone).
• Option c: $\frac{1}{3}\pi r^{2}$ is not a standard formula for the base area of a cone.
• Option d: $\pi r^{2}h$ is the volume formula of a cylinder.

Answer:

B. $\pi r^{2}$