Question

an oblique prism has hexagonal bases that are 4 centimeters along each side. the height of the prism is 3 centimeters. what is the volume of the prism? 2 of 4 questio 6\sqrt{3} cm³ 18\sqrt{3} cm³ 72\sqrt{3} cm³ 24\sqrt{3} cm³

Explanation:

Step1: Calculate the area of the hexagonal base

The formula for the area of a regular hexagon with side length \(s\) is \(A = \frac{3\sqrt{3}}{2}s^{2}\). Given \(s = 4\) cm, we substitute into the formula:
\(A=\frac{3\sqrt{3}}{2}\times4^{2}=\frac{3\sqrt{3}}{2}\times16 = 24\sqrt{3}\text{ cm}^{2}\)

Step2: Calculate the volume of the prism

The formula for the volume of a prism is \(V=Ah\), where \(A\) is the area of the base and \(h\) is the height. Given \(A = 24\sqrt{3}\text{ cm}^{2}\) and \(h = 3\) cm, we substitute into the formula:
\(V=(24\sqrt{3})\times3=72\sqrt{3}\text{ cm}^{3}\)

Answer:

\(72\sqrt{3}\text{ cm}^{3}\) (the third option)