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Date November 2019 Marks available 3 Reference code 19N.1.SL.TZ0.T_5
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Calculate Question number T_5 Adapted from N/A

Question

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]
a.

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]
b.

Markscheme

units are required in both parts

 

(V=)5×10×40+2×10×40          (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]

a.

units are required in both parts

 

2800=π×r2×30         (M1)(M1)

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

(r=) 5.45 cm  (5.45058… cm)        (A1)(ft)  (C3)

Note: Follow through from their part (a).

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.1—3d space, volume, angles, midpoints
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Topic 3—Geometry and trigonometry

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