Let's solve the problem step-by-step.
### 1. Understand the Problem
We are given:
- A pyramid with a square base
- The side length of the square base is [tex]\(4.6\)[/tex] meters
- The height of the pyramid is [tex]\(7.2\)[/tex] meters
We need to find the volume of the pyramid and round it to the nearest tenth of a cubic meter.
### 2. Relevant Formula
The volume [tex]\(V\)[/tex] of a pyramid with a square base is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
### 3. Calculate the Area of the Base
Since the base is a square with side length [tex]\(4.6\)[/tex] meters, the area [tex]\(A\)[/tex] of the base is:
[tex]\[ \text{Base Area} = \text{side length}^2 \][/tex]
Substituting the given side length:
[tex]\[ \text{Base Area} = 4.6^2 \][/tex]
[tex]\[ \text{Base Area} = 21.16 \, \text{square meters} \][/tex]
### 4. Calculate the Volume
Using the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Substituting the values we have:
[tex]\[ V = \frac{1}{3} \times 21.16 \, \text{m}^2 \times 7.2 \, \text{m} \][/tex]
### 5. Perform the Calculation
First, multiply the base area by the height:
[tex]\[ 21.16 \times 7.2 = 152.352 \][/tex]
Then divide by 3:
[tex]\[ V = \frac{152.352}{3} \][/tex]
[tex]\[ V = 50.784 \, \text{cubic meters} \][/tex]
### 6. Round to the Nearest Tenth
Finally, round [tex]\(50.784\)[/tex] to the nearest tenth.
The volume of the pyramid, rounded to the nearest tenth, is:
[tex]\[ V \approx 50.8 \, \text{cubic meters} \][/tex]
### Final Answer
The volume of the pyramid is approximately [tex]\(50.8\)[/tex] cubic meters.
