Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre
The ratio of the outer and inner perimeters of a circular path is 23: 22 If the
The ratio of the outer and inner perimeters of a circular path is 23: 22 If the path is \( 5 \mathrm{m} \) wide what is the diameter of the circle? Also find the area of path enclosed between the two circles.
- A. 3535.71 sq. \( \mathrm{m} \)
- B. 1232.23 sq. \( \mathrm{m} \)
- C. 2727.53 sq. \( \mathrm{m} \)
- D. 4343.12 sq. \( \mathrm{m} \)
Step-by-step solution
Let inner radius = r, outer radius = r+5. Ratio of perimeters = (2π(r+5))/(2πr) = 23/22 => (r+5)/r = 23/22 => r = 110 m, so outer radius = 115 m. Area of path = π(115^2 - 110^2) = π(13225 - 12100) = 1125π. Using π=22/7, area = 1125*(22/7) = 24750/7 ≈ 3535.71 sq. m.
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