Question

what measurement is essential for calculating the volume of a cylinder?
a. radius of the base
b. area of the side
c. an arc on the base
d. circumference of the base

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.

Step2: Analyze each option

• Option a: Since \(r\) (radius of the base) is in the volume formula \(V = \pi r^{2}h\), it is essential.
• Option b: The lateral - surface area formula is \(A = 2\pi rh\). It is not part of the volume formula \(V=\pi r^{2}h\).
• Option c: An arc length on the base (\(s = r\theta\)) is not relevant to the volume formula \(V=\pi r^{2}h\).
• Option d: The circumference formula is \(C = 2\pi r\). While \(r=\frac{C}{2\pi}\), the radius \(r\) (not the circumference) is directly in the volume formula \(V=\pi r^{2}h\).

Answer:

A. Radius of the base