In a park, a concrete walkway is built in the shape of a sector of a circular ring.…
MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
In a park, a concrete walkway is built in the shape of a sector of a circular ring. The outer radius of the ring is 18 m, while the inner radius (after construction) is (18−w) m, where w is the width of the walkway. The arc spanning the outer boundary of the walkway measures 31.5 m. The area of the walkway is 226.8m2.
(a) Establish an equation in θ (in degrees) relating the given arc length and the known outer radius.
(b) Using the value of θ obtained from part (a), set up an equation in w using the given area of the walkway.
(c) Solve the equations to find the numerical values of θ and w.
(d) Comment on whether the width you have obtained is practical if the park authorities require the walkway to be at least 2 m wide.