Question

a solid right pyramid has a regular hexagonal base with an area of ( 5.2 mathrm{~cm}^{2} ) and a height of ( h mathrm{~cm} ). which expression represents the volume of the pyramid? ( \frac{1}{5}(5.2) h mathrm{~cm}^{3} ) ( \frac{1}{5 h}(5.2) h mathrm{~cm}^{3} ) ( \frac{1}{3}(5.2) h mathrm{~cm}^{3} ) ( \frac{1}{3 h}(5.2) h mathrm{~cm}^{3} )

Explanation:

Step1: Recall the volume formula for a pyramid

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

Step2: Substitute the given values into the formula

Given that \( B = 5.2\mathrm{cm}^2 \) and the height is \( h\mathrm{cm} \). Substituting these values into the formula \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}(5.2)h\mathrm{cm}^3 \).

Answer:

\(\frac{1}{3}(5.2)h\mathrm{cm}^3\) (the third option)