SPM.2.SL.TZ0.1

pestleMathematicsAASLPaper 2SPM· sl-3-1-3d-space-volume-angles-distance-midpointssource ↗

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 / solution

$\frac{4}{3}\pi {\left( {12.7} \right)^3}$ (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]