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Date	May Specimen paper	Marks available	3	Reference code	SPM.2.SL.TZ0.1
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	1	Adapted from	N/A

Question

A metal sphere has a radius 12.7 cm.

Find the volume of the sphere expressing your answer in the form $a \times {10^k}$ , $1 \leqslant a < 10$ and $k \in \mathbb{Z}$ .

[3]

The sphere is to be melted down and remoulded into the shape of a cone with a height of 14.8 cm.

Find the radius of the base of the cone, correct to 2 significant figures.

[3]

Markscheme

$\frac{4}{3}\pi {\left( {12.7} \right)^3}$ (or equivalent) A1

8580.24 (A1)

V = 8.58 × 10³ A1

[3 marks]

recognising volume of the cone is same as volume of their sphere (M1)

$\frac{1}{3}\pi {r^2}\,\left( {14.8} \right) =$ 8580.24 (or equivalent) A1

r = 23.529

r = 24 (cm) correct to 2 significant figures A1

[3 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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22M.2.SL.TZ1.7d:
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Topic 3— Geometry and trigonometry

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