Question Show Examples Find the volume of a pyramid with a square base, where the perimeter of the base is $14.6 \mathrm{~m}$ and the height of the pyramid is $22.3 \mathrm{~m}$. Round your answer to the nearest tenth of a cubic meter. Answer Attempt 1 out of 2
Solution
Step 1 ：Given that the perimeter of the base of the pyramid is 14.6 m and the height of the pyramid is 22.3 m.
Step 2 ：The formula for the volume of a pyramid is \(V = \frac{1}{3} \times \text{base area} \times \text{height}\).
Step 3 ：Since the base of the pyramid is a square, the length of one side can be found by dividing the perimeter by 4. So, \(\text{side length} = \frac{\text{perimeter}}{4} = \frac{14.6}{4} = 3.65 \text{ m}\).
Step 4 ：The area of the base can be calculated by squaring the length of one side. So, \(\text{base area} = \text{side length}^2 = 3.65^2 = 13.3225 \text{ m}^2\).
Step 5 ：Substitute the base area and the height into the volume formula, we get \(V = \frac{1}{3} \times 13.3225 \times 22.3 = 99.0 \text{ m}^3\).
Step 6 ：\(\boxed{99.0}\) cubic meters is the volume of the pyramid.
