PSLE The figure shows a path of width 3 m in a rectangular park of length 33 m. The outline of the path is made up of quarter circles with centre P, semicircles with centre S and straight lines. PQ = RS.
- 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 = 33 m
Length of 3 radii of the smaller circle
= 33 - 3 - 3
= 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 3
= 24 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 9 + 3
= 12 m
Area of the big quadrant
=
14 x 3.14 x 12 x 12
= 113.04 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
= 113.04 - 63.585
= 49.455 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 3 x 12
= 36 m
2 Area of 3 curves
= 3 x 49.455
= 148.365 m
2 Area of the path
= 148.365 + 36
= 184.365 m
2 Answer(s): (a) 24 m; (b) 184.365 m
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