To find the volume of a pyramid with a square base, we can use the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Here's the step-by-step solution:
1. Identify the given values:
- The area of the base of the pyramid, [tex]\( A \)[/tex], is given as 8.7 square meters.
- The height of the pyramid, [tex]\( h \)[/tex], is given as 10 meters.
2. Plug the given values into the pyramid volume formula:
[tex]\[ V = \frac{1}{3} \times 8.7 \, \text{m}^2 \times 10 \, \text{m} \][/tex]
3. Perform the multiplication inside the formula:
[tex]\[ V = \frac{1}{3} \times 87 \, \text{m}^3 \][/tex]
4. Divide by 3 to find the volume:
[tex]\[ V = 29 \, \text{m}^3 \][/tex]
5. Round the volume to the nearest tenth:
Since 29 is already an integer, the nearest tenth in this case simply remains [tex]\( 29.0 \, \text{m}^3 \)[/tex].
Therefore, the volume of the pyramid is [tex]\( 29.0 \, \text{m}^3 \)[/tex], rounded to the nearest tenth.
