Question

which of these mathematical constants or numbers is crucial when calculating the volume of a cylinder?
a. $phi$ (golden ratio)
b. $pi$ (pi)
c. $e$ (eulers number)
d. $sqrt{2}$ (square root of 2)

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 of the cylinder.

Step2: Analyze each option

• Option a: The golden ratio \(\Phi=\frac{1 + \sqrt{5}}{2}\approx1.618\) is not used in the formula for the volume of a cylinder.
• Option b: In the formula \(V = \pi r^{2}h\), \(\pi\) (Pi) is present.
• Option c: Euler's number \(e\approx2.718\) is not used in the formula for the volume of a cylinder.
• Option d: \(\sqrt{2}\approx1.414\) is not used in the formula for the volume of a cylinder.

Answer:

B. \(\pi\) (Pi)