Question

a solid right pyramid has a regular hexagonal base with an area of 5.2 cm² and a height of h cm. which expression represents the volume of the pyramid? 〇 \\(\frac{1}{5}(5.2)h\\) cm³ 〇 \\(\frac{1}{5h}(5.2)h\\) cm³ 〇 \\(\frac{1}{3}(5.2)h\\) cm³ 〇 \\(\frac{1}{3h}(5.2)h\\) cm³

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Identify the base area and height

In this problem, the area of the base \( B = 5.2\space cm^{2}\) and the height of the pyramid is \( h\space cm\).

Step3: Substitute the values into the formula

Substituting \( B = 5.2\) and \( h\) (the height of the pyramid) into the volume formula \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}(5.2)h\space cm^{3}\).

Answer:

\(\boldsymbol{\frac{1}{3}(5.2)h\space cm^{3}}\) (the third option: \(\frac{1}{3}(5.2)h\space cm^{3}\))