Find the volume of a pyramid with a square base, where the area of the base is 8.3 m² and the height of the pyramid is 9.8 m. Round your answer to the nearest tenth of a cubic mete... Find the volume of a pyramid with a square base, where the area of the base is 8.3 m² and the height of the pyramid is 9.8 m. Round your answer to the nearest tenth of a cubic meter.
Understand the Problem
The question asks us to calculate the volume of a pyramid with a square base. We are given the area of the base and the height of the pyramid. We will apply the formula for the volume of a pyramid, which is V = (1/3) * base area * height, and then round the result to the nearest tenth.
Answer
$27.1 \text{ m}^3$
Answer for screen readers
$27.1 \text{ m}^3$
Steps to Solve
- Write the formula for the volume of a pyramid
The volume $V$ of a pyramid is given by the formula: $$ V = \frac{1}{3} \times \text{base area} \times \text{height} $$
- Plug in the given values
We are given that the base area is $8.3 \text{ m}^2$ and the height is $9.8 \text{ m}$. Plugging these values into the formula gives: $$ V = \frac{1}{3} \times 8.3 \text{ m}^2 \times 9.8 \text{ m} $$
- Calculate the volume
$$ V = \frac{1}{3} \times 81.34 \text{ m}^3 $$ $$ V = 27.11333... \text{ m}^3 $$
- Round to the nearest tenth
Rounding $27.11333...$ to the nearest tenth gives $27.1$.
$27.1 \text{ m}^3$
More Information
The volume of the pyramid is approximately $27.1$ cubic meters.
Tips
A common mistake is forgetting to divide by 3 in the volume formula for a pyramid. Another common mistake is incorrectly rounding the final answer. Always double-check your calculations and rounding.
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