Sure, let's calculate the volume of the pyramid using the given formula [tex]\( V = \frac{1}{3} \times A \times h \)[/tex], where [tex]\( A \)[/tex] is the area of the base and [tex]\( h \)[/tex] is the height.
Step-by-Step Solution:
1. Determine the dimensions of the base:
- The width of the base is 5 feet.
- The length of the base is 3 feet.
2. Calculate the area of the base ([tex]\( A \)[/tex]):
The base is a rectangle, so the area can be calculated using the formula for the area of a rectangle:
[tex]\[
A = \text{width} \times \text{length}
\][/tex]
Substituting the dimensions, we get:
[tex]\[
A = 5 \, \text{feet} \times 3 \, \text{feet} = 15 \, \text{square feet}
\][/tex]
3. Given the height ([tex]\( h \)[/tex]) of the pyramid:
The height of the pyramid is 8 feet.
4. Calculate the volume of the pyramid ([tex]\( V \)[/tex]):
Using the formula for the volume of a pyramid:
[tex]\[
V = \frac{1}{3} \times A \times h
\][/tex]
Substituting the values we've determined:
[tex]\[
V = \frac{1}{3} \times 15 \, \text{square feet} \times 8 \, \text{feet}
\][/tex]
5. Perform the multiplication:
First multiply the area of the base by the height:
[tex]\[
15 \, \text{square feet} \times 8 \, \text{feet} = 120 \, \text{cubic feet}
\][/tex]
Then, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
V = \frac{1}{3} \times 120 \, \text{cubic feet} = 40 \, \text{cubic feet}
\][/tex]
Therefore, the area of the base is [tex]\( 15 \, \text{square feet} \)[/tex] and the volume of the pyramid is [tex]\( 40 \, \text{cubic feet} \)[/tex].
