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Date	May 2018	Marks available	4	Reference code	18M.1.SL.TZ2.T_15
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 2
Command term	Calculate	Question number	T_15	Adapted from	N/A

Question

Julio is making a wooden pencil case in the shape of a large pencil. The pencil case consists of a cylinder attached to a cone, as shown.

The cylinder has a radius of r cm and a height of 12 cm.

The cone has a base radius of r cm and a height of 10 cm.

Find an expression for the slant height of the cone in terms of r.

[2]

The total external surface area of the pencil case rounded to 3 significant figures is 570 cm².

Using your graphic display calculator, calculate the value of r.

[4]

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(slant height² =) 10² + r ² (M1)

Note: For correct substitution of 10 and r into Pythagoras’ Theorem.

$\sqrt {{{10}^2} + {r^2}}$ (A1) (C2)

[2 marks]

$\pi {r^2} + 2\pi r \times 12 + \pi r\sqrt {100 + {r^2}} = 570$ (M1)(M1)(M1)

Note: Award (M1) for correct substitution in curved surface area of cylinder and area of the base, (M1) for their correct substitution in curved surface area of cone, (M1) for adding their 3 surface areas and equating to 570. Follow through their part (a).

= 4.58 (4.58358...) (A1)(ft) (C4)

Note: Last line must be seen to award final (A1). Follow through from part (a).

[4 marks]

Examiners report

[N/A]

Syllabus sections

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

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Topic 3— Geometry and trigonometry

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