Figure $1$ shows an open trough in the form of a trapezoidal prism. $AD=HG=100$ cm, $BC=EF=50$

Question

Figure $1$ shows an open trough in the form of a trapezoidal prism. $AD=HG=100$ cm, $BC=EF=50$ cm, $JE=80$ cm, $AB=DC=GF=HE=83.82$ cm and $CF=200$ cm. The trough is filled to the brim with water. Calculate the volume of the water in the trough. The trough is to be painted on its external surfaces, calculate the total area of the external surfaces to be painted. All the water from the trough is then transferred into an open cylindrical container as shown in Figure $2$. The base of this cylinder has a circumference of $440$ cm. Calculate the height of the water, $h$, in the cylinder. $\left( \mathrm{Take }\pi =\frac{22}{7} \right)$.

Accepted Answer

(a) $1\,200\,000\text{ cm}^3$ (3 s.f.) (b) $55\,500\text{ cm}^2$ (3 s.f.) (c) $77.9\text{ cm}$ (3 s.f.)

Volume and Surface Area of a Trapezoidal Trough

Volume and Surface Area of a Trapezoidal Trough

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