A decorative border is made of 4 identical semicircular tiles. Their diameters lie end to end along a straight edge PQ of 40 cm.
- Find the radius of one tile.
- Find the total area of the 4 tiles. Leave your answer in terms of π.
Need a hint?
Find the diameter of one tile first by sharing the 40 cm among the 4 tiles. Then halve the diameter to get the radius.
Worked answer
- (a) 4 diameters make 40 cm, so one diameter is 40 ÷ 4 = 10 cm.
- (a) Radius = 10 ÷ 2 = 5 cm.
- (b) Area of one full circle = π × 5 × 5 = 25π cm².
- (b) Area of one semicircle = 25π ÷ 2 = 12.5π cm².
- (b) Total area of 4 tiles = 4 × 12.5π = 50π cm².
Answer: 50π cm²
The mistake this question tests
Habit
Radius and diameter in circles
Pupils often use the 40 cm as the diameter of each tile, or forget to halve the full circle area, which gives an answer far larger than 50π.
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