19N.1.SL.TZ0.T_5

pestleMathematicsAISLPaper 119N· sl-3-1-3d-space-volume-angles-midpointssource ↗

Yao drains the oil from his motorbike into two identical cuboids with rectangular bases of width $10$ cm and length $40$ cm. The height of each cuboid is $5$ cm.

The oil from the motorbike fills the first cuboid completely and the second cuboid to a height of $2$ cm. The information is shown in the following diagram.

Calculate the volume of oil drained from Yao’s motorbike.

[3]

Yao then pours all the oil from the cuboids into an empty cylindrical container. The height of the oil in the container is $30$ cm.

Find the internal radius, $r$ , of the container.

[3]

Markscheme / solution

units are required in both parts

$\left( {V = } \right)\,\,5 \times 10 \times 40 + 2 \times 10 \times 40$ (M1)(M1)

Note: Award (M1) for correct substitutions in volume formula for both cuboids. Award (M1) for adding the volumes of both cuboids.

$2800$ cm³ (A1) (C3)

[3 marks]

units are required in both parts

$2800 = \pi \times {r^2} \times 30$ (M1)(M1)

Note: Award (M1) for correct substitution in volume of cylinder formula. Award (M1) for equating their expression (must include $\pi$ and $r$ ) to their $2800$ .

$\left( {r = } \right)$ $5.45$ cm ( $5.45058$ … cm) (A1)(ft) (C3)

Note: Follow through from their part (a).

[3 marks]

Examiners’ report

[N/A]