Question

a tent is shaped like a hexagonal pyramid. the area of the hexagonal base is equal to 64.95 ft², and the volume of the tent is 281.46 ft³. what is the height of the tent, rounded to the nearest foot? 4.3 feet 6.5 feet 13.0 feet 14.7 feet

Explanation:

Step1: Recall volume formula for pyramid

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

Step2: Rearrange formula for height

We can rewrite the formula to solve for $h$: $h = \frac{3V}{B}$.

Step3: Substitute given values

Given $V = 281.46$ ft³ and $B=64.95$ ft². Substitute into the formula: $h=\frac{3\times281.46}{64.95}$.
First, calculate $3\times281.46 = 844.38$. Then, $h=\frac{844.38}{64.95}=13$.

Answer:

13.0 feet