Subjects geometry

Trapezoidal Prism Volume A79707

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1. **State the problem:** We need to find the volume of a trapezoidal prism with the following dimensions: top base $= 55$ m, bottom base $= 25$ m, height of trapezoid $= 20$ m, and prism height (length) $= 18$ m. 2. **Formula for volume of a trapezoidal prism:** The volume $V$ is given by the area of the trapezoidal base times the height (length) of the prism: $$V = A_{base} \times h_{prism}$$ where $$A_{base} = \frac{(b_1 + b_2)}{2} \times h_{trap}$$ Here, $b_1$ and $b_2$ are the lengths of the two parallel sides of the trapezoid, and $h_{trap}$ is the height of the trapezoid. 3. **Calculate the area of the trapezoidal base:** $$A_{base} = \frac{(55 + 25)}{2} \times 20 = \frac{80}{2} \times 20 = 40 \times 20 = 800 \text{ m}^2$$ 4. **Calculate the volume of the prism:** $$V = 800 \times 18 = 14400 \text{ m}^3$$ 5. **Interpretation:** The volume of the water tank is $14400$ cubic meters, meaning it can hold that much water if filled completely. **Final answer:** $$\boxed{14400 \text{ m}^3}$$