NCERT Solutions Class 10 Mathematics Solutions for Areas Related to Circles - Exercise 12.3 in Chapter 12 - Areas Related to Circles
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The given figure depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find the area of the track.
Width of the track = 10 m
Distance between two parallel lines = 60 m
Length of parallel tracks = 106 m
DE = CF = 60 m
Radius of inner semicircle, r = OD = O’C
= 60/2 m = 30 m
Radius of outer semicircle, R = OA = O’B
= 30+10 m = 40 m
Also, AB = CD = EF = GH = 106 m
Distance around the track along its inner edge = CD+EF+2×(Circumference of inner semicircle)
= 106+106+(2×πr) = 212+(2×\frac{22}{7}×30)\\ = 212+\frac{1320}{7} = \frac{2804}{7} \\ \text{Area of the track}= \text{Area of ABCD + Area EFGH} + 2 × (\text{area of outer semicircle}) - 2×(\text{area of inner semicircle})\\ = (AB×CD)+(EF×GH)+2×(πr^2) -2×(πR^2)\\ = (106×10)+(106×10)+2×\fracπ2(r^2-R^2)\\ = 2120+\frac{22}{7}×70×10\\ = 4320\ m^2
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