21M.1.SL.TZ2.3

pestleMathematicsAISLPaper 121M· sl-3-1-3d-space-volume-angles-midpointssource ↗

A storage container consists of a box of length $90 cm$ , width $42 cm$ and height $34 cm$ , and a lid in the shape of a half-cylinder, as shown in the diagram. The lid fits the top of the box exactly. The total exterior surface of the storage container is to be painted.

Find the area to be painted.

Markscheme / solution

$2 \times 90 \times 34 (= 6120)$ AND $2 \times 42 \times 34 (= 2856)$ (A1)

$90 \times 42 (= 3780)$ (A1)

$r = 21$ (A1)

$π \times 21^{2} (= 441 π, 1385.44 \dots)$ (M1)

use of curved surface area formula (M1)

$21 π \times 90 (= 1890 π, 5937.61 \dots)$ (A1)

$20100 {cm}^{2} (20079.0 \dots)$ A1

[7 marks]

Examiners’ report

[N/A]