The inner circumference of a circular track is 176 m. The track is 7 m wide. Calculate the (a) area of the track. (b) cost of putting up a fence along the outer circle at the rate of 12 per metre. (Use л= 22 7
Question
The inner circumference of a circular track is 176 m. The track is 7 m wide. Calculate the (a) area of the track. (b) cost of putting up a fence along the outer circle at the rate of 12 per metre. (Use л= 22 7
Solution
Sure, let's solve this step by step.
(a) Area of the track
First, we need to find the radius of the inner circle. We know that the circumference of a circle is given by 2πr, where r is the radius. So, the radius of the inner circle is 176/(2π) = 28 m.
The track is 7 m wide, so the radius of the outer circle is 28 + 7 = 35 m.
The area of the track is the difference between the area of the outer circle and the inner circle. The area of a circle is given by πr².
So, the area of the outer circle is π*(35)² = 3850 m² and the area of the inner circle is π*(28)² = 2464 m².
Therefore, the area of the track is 3850 - 2464 = 1386 m².
(b) Cost of putting up a fence along the outer circle
The length of the fence is equal to the circumference of the outer circle, which is 2πr = 2π*35 = 220 m.
The cost of the fence is 12 per metre, so the total cost is 220*12 = 2640.
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