Subjects geometry

Volume Prism C53C07

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Find the volume of the prism given that it has the same base and height as a pyramid, and the prism's volume is 3 times the volume of the pyramid. 2. **Recall the formulas:** - Volume of a pyramid: $$V_{pyramid} = \frac{1}{3} B h$$ where $B$ is the base area and $h$ is the height. - Volume of a prism: $$V_{prism} = B h$$ 3. **Given:** - Volume of the pyramid: $312$ cubic feet. - Volume of the prism is 3 times the volume of the pyramid. 4. **Calculate the volume of the prism:** $$V_{prism} = 3 \times V_{pyramid} = 3 \times 312 = 936$$ cubic feet. 5. **Explanation:** Since the prism has the same base and height as the pyramid, but the pyramid's volume formula includes the factor $\frac{1}{3}$, the prism's volume is exactly 3 times larger. **Final answer:** $$\boxed{936 \text{ cubic feet}}$$