A solid right pyramid has a regular hexagonal base with an area of [tex]$5.2 \, \text{cm}^2$[/tex] and a height of [tex]$h \, \text{cm}$[/tex].

Which expression represents the volume of the pyramid?

A. [tex]\frac{1}{5}(5.2) h \, \text{cm}^3[/tex]
B. [tex]\frac{1}{5 h}(5.2) h \, \text{cm}^3[/tex]
C. [tex]\frac{1}{3}(5.2) h \, \text{cm}^3[/tex]
D. [tex]\frac{1}{3 h}(5.2) h \, \text{cm}^3[/tex]



Answer :

To find the volume of a pyramid, we can use the formula:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

In this particular pyramid, we're given:
- The base area [tex]\( A = 5.2 \, \text{cm}^2 \)[/tex]
- The height [tex]\( h \, \text{cm} \)[/tex]

We need to substitute these values into the volume formula.

[tex]\[ V = \frac{1}{3} \times 5.2 \times h \][/tex]

Simplifying this expression, we get:

[tex]\[ V = \frac{1}{3} \times 5.2 \times h \, \text{cm}^3 \][/tex]

Therefore, the expression that represents the volume is:

[tex]\[ \frac{1}{3}(5.2) h \, \text{cm}^3 \][/tex]

So, the correct option is:

[tex]\[ \boxed{\frac{1}{3}(5.2) h \, \text{cm}^3} \][/tex]