A tent is in the shape of a square pyramid. The side length of the tent’s base is 9 feet, and the tent's height is 6.5 feet. What is the volume of the tent in cubic feet?

Answer 1

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

\[ V = \frac{1}{3} \cdot B \cdot h \]

where \(V\) is the volume, \(B\) is the area of the base, and \(h\) is the height of the pyramid.

1. Calculate the area of the base \(B\). Since the base is a square with a side length of 9 feet, the area \(B\) is calculated as follows:

\[ B = \text{side length}^2 = 9^2 = 81 \text{ square feet} \]

2. The height \(h\) of the tent is given as 6.5 feet.

3. Substituting \(B\) and \(h\) into the volume formula:

\[ V = \frac{1}{3} \cdot 81 \cdot 6.5 \]

4. First, calculate \(81 \cdot 6.5\):

\[ 81 \cdot 6.5 = 526.5 \]

5. Now plug in this value into the volume formula:

\[ V = \frac{1}{3} \cdot 526.5 \]

6. Finally, calculate \(\frac{526.5}{3}\):

\[ V = 175.5 \]

Thus, the volume of the tent is

\[ \boxed{175.5} \text{ cubic feet} \]