Question

1. which of these mathematical constants or numbers is crucial when calculating the volume of a cylinder?

a. √2 (square root of 2)
b. φ (golden ratio)
c. e (eulers number)
d. π (pi)

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Analyze each option

• Option a: \(\sqrt{2}\) is not present in the formula \(V = \pi r^{2}h\).
• Option b: The golden ratio \(\Phi\) is not part of the volume formula for a cylinder.
• Option c: Euler's number \(e\) is not in the formula \(V=\pi r^{2}h\).
• Option d: \(\pi\) is a crucial part of the formula \(V=\pi r^{2}h\) as it is multiplied by the square of the radius and the height.

Answer:

d. \(\pi\) (Pi)