Mathematics 0580 · IGCSE · Surface area and volume

Surface area and volume — practice question

The diagram depicts a horizontal water trough shaped as a prism. Its cross-section is a trapezium. The trapezium’s parallel sides measure 35 cm and 25 cm, and its perpendicular height is 12 cm. The prism extends for 120 cm.
(a)[3]

Calculate the volume of the trough.

(b(i))[2]

Show that the volume of water is $19800\text{ cm}^3$.

(b(ii))[1]

Calculate the percentage of the trough that contains water.

(c)[4]

Calculate the time taken to empty the trough. Give your answer in hours and minutes.

(d)[3]

Calculate the value of $r$.

(e)[2]

Calculate the combined mass of the cylinder and the water. Give your answer in kilograms.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use the trapezium rule: $0.5(35+25)\times12\times120$.

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