PSLE The figure shows a path of width 2 m in a rectangular park of length 31 m. The outline of the path is made up of quarter circles with centre W, semicircles with centre Z and straight lines. WX = YZ.
- What is the width of the rectangular park?
- Find the area of the path. Take π = 3.14
(a)
Length of 3 radii of the smaller circle + 2 widths of the path = 31 m
Length of 3 radii of the smaller circle
= 31 - 2 - 2
= 27 m
Radius of the smaller circles
= 27 ÷ 3
= 9 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 9 + 2 x 2
= 22 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 9 + 2
= 11 m
Area of the big quadrant
=
14 x 3.14 x 11 x 11
= 94.985 m
2 Area of the small quadrant
=
14 x 3.14 x 9 x 9
= 63.585 m
2 Area of the path in one curve
= 94.985 - 63.585
= 31.4 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 2 x 11
= 22 m
2 Area of 3 curves
= 3 x 31.4
= 94.2 m
2 Area of the path
= 94.2 + 22
= 116.2 m
2 Answer(s): (a) 22 m; (b) 116.2 m
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