Question

a trough 15 m long and has bottom 30 cm and 60 cm. its cross-section is a trapezium. find its volume

Answer 1

Answer on Question #56336 – Math – Geometry

A trough 15 m long and has bottom 30 cm and 60 cm. Its cross-section is a trapezium. Find its volume.

Solution (case 1):

The problem did not specify the height of the trough, so let it be X.

We cut our figure into two. The volume of the parallelepiped is $1500 \cdot 30x = 45000x \, \text{cm}^3$

The volume of the pyramid is $0.5 \cdot 1500 \cdot 30x = 22500x \, \text{cm}^3$ .

The volume of the trough is $45000 \times 22500 \times 67500 \times \mathrm{cm}^3$ .

Answer: $67500 \times \mathrm{cm}^3$ , where $x$ is the height of the trough.

Solution (case 2):

If this interpretation of conditions is true, then the volume of the trough will be equal as follows:

$$\begin{array}{l} V = \frac {1}{3} \pi H \left(R _ {1} ^ {2} + R _ {1} R _ {2} + R _ {2} ^ {2}\right) = \frac {1}{3} \pi \cdot 1 5 0 0 \cdot \left(3 0 ^ {2} + 3 0 \cdot 6 0 + 6 0 ^ {2}\right) = 3 1 5 0 0 0 0 \pi \\ \approx 9 8 9 6 0 1 7 \approx 9 9 0 0 0 0 0 c m ^ {3} = 9. 9 m ^ {3} = 9 9 0 0 l i t e r \\ \end{array}$$

Answer:

$$9\,900\,000\,\mathrm{cm}^3 = 9.9\,\mathrm{m}^3 = 9\,900\,\mathrm{liter}$$

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