Certainly! Let's break down the problem step-by-step to find the volume of a square pyramid with a given base area and height:
1. Identify the given values:
- The area of the base ([tex]\(A\)[/tex]) of the square pyramid is 441 square feet.
- The height ([tex]\(h\)[/tex]) of the pyramid is 24 feet.
2. Recall the formula for the volume of a square pyramid:
[tex]\[
\text{Volume} = \frac{1}{3} \times (\text{Base Area}) \times (\text{Height})
\][/tex]
Here, substituting the given values:
[tex]\[
\text{Volume} = \frac{1}{3} \times 441 \text{ ft}^2 \times 24 \text{ ft}
\][/tex]
3. Calculate the volume:
[tex]\[
\text{Volume} = \frac{1}{3} \times 441 \times 24
\][/tex]
4. Break it down further:
[tex]\[
441 \times 24 = 10584
\][/tex]
[tex]\[
\frac{1}{3} \times 10584 = 3528 \text{ ft}^3
\][/tex]
5. Round the volume to the nearest tenth:
- The volume, calculated as [tex]\(3528\)[/tex] cubic feet, is already a whole number.
- Thus, when rounded to the nearest tenth, it remains [tex]\(3528.0\)[/tex] cubic feet.
Therefore, the volume of the square pyramid, rounded to the nearest tenth, is [tex]\(3528.0\)[/tex] cubic feet.
