A square tile ABCD has sides of 10 cm. A quarter circle with centre A and radius 10 cm is cut out of the tile, so its curved edge runs from B to D. The shaded piece is the part of the tile that remains after the quarter circle is removed. Take π = 3.14.
- Find the length of the curved edge BD. [2]
- Find the area of the shaded piece. [2]
Need a hint?
For (a), a quarter circle has only one quarter of the full circumference. For (b), find the square's area first, then take away the quarter circle's area.
Worked answer
- (a) The curved edge BD is one quarter of a full circle of radius 10 cm.
- (a) Full circumference = 2 × 3.14 × 10 = 62.8 cm.
- (a) Length of BD = 62.8 ÷ 4 = 15.7 cm.
- (b) Area of the square = 10 × 10 = 100 cm².
- (b) Area of the quarter circle = 3.14 × 10 × 10 ÷ 4 = 78.5 cm².
- (b) Shaded area = 100 − 78.5 = 21.5 cm².
The mistake this question tests
Area and perimeter formulas
Pupils often use the full circumference 62.8 cm in (a), or subtract a full circle's area (314) from the square in (b).
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