Mensuration-24

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(a)A race track is in the form of a ring whose inner circumference is 352 m, and the outer circumference is 396 m.
Find the width of the track.

(b) The inner circumference of a circular track is 220 m. The track is 7 meter wide everywhere.
Calculate the cost of putting up a fence along the outer circle at the rate of $ 2 per meter.

Solution: (a) Let the outer and inner radii of the ring be R meters and r meters respectively.

It is given that 2 Π R = 396 and 2 Π r = 352

=> 2 x 22 / 7 x R = 396 and 2 x 22 / 7 x r = 352

=> R = 396 x 7 / (2 x 22) m = 63 m and r = 352 x 7 / (2 x 22) m = 56 m

Hence, width of the track = (R - r) meters = (63 - 56) m = 7 m

(b) Inner circumference = 220 m

=> 2 Π r = 220; 2 x 22 / 7 x r = 220

=> r = 220 x 7 / (2 x 22) = 35 m

Since the track is 7 meter wide everywhere, therefore,

Outer radius R = r + 7 = (35 + 7) m = 42 m

Therefore, Outer circumference = 2 Π R = (2 x 22 / 7 x 42) m = 264 m

Rate of fencing = $ 2 per meter

Therefore, Total cost of fencing = $ (264 x 2) = $ 528.

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