Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

(a(i))[2]

Determine the length and width of rectangle $R$.

(a(ii))[2]

Rectangle $S$ is mathematically similar to rectangle $R$. The perimeter of rectangle $S$ is $30.6\text{ cm}$. Calculate the length of rectangle $S$.

(b(i))[2]

A piece of card is a sector of a circle with sector angle $75^\f$ and radius $8\text{ cm}$. Find an expression, in terms of $\pi$, for the arc length of the sector.

(b(ii))[5]

The card makes the curved surface area of a cone. The cone is completely filled with water. Calculate the volume of water in the cone. (Volume of a cone $= \frac{1}{3}\pi r^2 h$.)

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: The length is $6.8$ and the width is $3.4$.

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