To find the volume of a pyramid with a given base area and height, we use the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this problem, we are given:
- The area of the base ([tex]\( \text{Base Area} \)[/tex]) is 19.8 square inches.
- The height of the pyramid ([tex]\( \text{Height} \)[/tex]) is 16.4 inches.
Let's plug these values into the formula and calculate the volume step by step:
1. Write down the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
2. Substitute the given values:
[tex]\[ V = \frac{1}{3} \times 19.8 \, \text{in}^2 \times 16.4 \, \text{in} \][/tex]
3. Calculate the product of the base area and height:
[tex]\[ 19.8 \times 16.4 = 324.72 \][/tex]
4. Multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ V = \frac{1}{3} \times 324.72 \][/tex]
5. Compute the final volume:
[tex]\[ V = 108.24 \, \text{cubic inches} \][/tex]
6. Round the volume to the nearest tenth:
[tex]\[ V \approx 108.2 \, \text{cubic inches} \][/tex]
Therefore, the volume of the pyramid, rounded to the nearest tenth of a cubic inch, is 108.2 cubic inches.
