SPM.1.SL.TZ0.11

pestleMathematicsAISLPaper 1SPM· sl-3-1-3d-space-volume-angles-midpointssource ↗

Helen is building a cabin using cylindrical logs of length 2.4 m and radius 8.4 cm. A wedge is cut from one log and the cross-section of this log is illustrated in the following diagram.

Find the volume of this log.

Markscheme / solution

volume $= 240\left( {\pi \times {{8.4}^2} - \frac{1}{2} \times {{8.4}^2} \times 0.872664 \ldots } \right)$ M1M1M1

Note: Award M1 240 × area, award M1 for correctly substituting area sector formula, award M1 for subtraction of their area of the sector from area of circle.

= 45800 (= 45811.96071) A1

[4 marks]

Examiners’ report

[N/A]