Question

A necklace is made up of wooden beads. Each bead is in the form of a sphere of diameter 4.2 mm. A cylinder is hollowed out from each bead. If the radius of the cylinder is 1 mm, find the volume of wood left in each bead.

Approach

Radius of sphere R = 2.1 mm, radius of cylinder r = 1 mm, height h = 4.2 mm. Volume = $\frac{4}{3} π R^{3} - π r^{2} h = \frac{4}{3} \times \frac{22}{7} \times 2. 1^{3} - \frac{22}{7} \times 1^{2} \times 4.2 \approx 25.608$ cu. mm.

Step-by-step working

1
Radius of sphere R = 2.1 mm, radius of cylinder r = 1 mm, height h = 4.2 mm
1 mark
2
Volume = $\frac{4}{3} π R^{3} - π r^{2} h$
1 mark
3
= $\frac{4}{3} \times \frac{22}{7} \times 2.1 \times 2.1 \times 2.1 - \frac{22}{7} \times 1 \times 1 \times 4.2$
2 marks
4
= 25.608 cu. mm
1 mark

Concepts used

volumespherecylindermensuration

Approach

Step-by-step working

Concepts used

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