In the adjoining figure, the inside perimeter of a running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.
Mensuration
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Question

In the adjoining figure, the inside perimeter of a running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.

Mensuration

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KnowledgeBoat · Accepted Answer

Given, Inside perimeter of the track = 312 m Straight portions = 90 m each Width of track = 2 m Let inner radius be 'r' and outer radius be 'R'. Inside perimeter consists of : Two straights lengths = 90 + 90 = 180 Two semicircles = one full circle So, ⇒ 180 + 2πr = 312 ⇒ 2πr = 312 - 180 ⇒ 2πr = 132 ⇒ 2 × × r = 132 ⇒ r = ⇒ r = 21 m. Outer radius (R) = r + 2 = 21 + 2 = 23 m. Area of straight rectangular parts: Area = 2 × (90 × 2) = 360 m2. Area of curved part : Area = π(R2 - r2) = π(232 - 212) = π(529 - 441) = 88π = 88 × = 276.57 m2. Total area of track = 360 + 276.57 = 636.57 m2. Hence, area of track = 636.57 m2.

Mathematics

In the adjoining figure, the inside perimeter of a running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.

Mensuration

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