Question

the area of the base of a cylinder is calculated by: a. \\( \frac { 4 } { 3 } \pi r ^ { 3 } \\) b. \\( 2 \pi r h \\) c. \\( \pi r ^ { 2 } \\) d. \\( 2 \pi r \\)

Explanation:

Step1: Recall the formula for the area of a circle

The base of a cylinder is a circle. The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Analyze each option

• Option a: \(\frac{4}{3}\pi r^{3}\) is the formula for the volume of a sphere.
• Option b: \(2\pi rh\) is the formula for the lateral (curved) surface area of a cylinder.
• Option c: \(\pi r^{2}\) is the formula for the area of a circle (base of the cylinder).
• Option d: \(2\pi r\) is the formula for the circumference of a circle.

Answer:

C. \(\pi r^{2}\)