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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 × r 2 × 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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