Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

The diagram represents a tank. It is a cuboid with length $1.2\,\text{m}$, width $0.6\,\text{m}$ and height $h\,\text{m}$. Its volume is $1.8\,\text{m}^3$.
(a(i))[2]

Calculate $h$.

(a(ii))[3]

Fuel is pumped into the empty tank at a rate of $0.2\,\text{m}^3$ per minute. Calculate the time taken to fill the tank to $90\%$ of its volume. Give your answer in minutes and seconds.

(b)[5]

The diagram shows an open-topped tank. The tank is a prism with trapezium $ABCD$ as its cross-section. $AD = BC = 70\,\text{cm}$, $CD = 80\,\text{cm}$ and $AB = 110\,\text{cm}$. The base of the tank is a square. Calculate the total surface area of the outside of the tank.

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