Radius of the larger circle, R = 21 cm

Radius of the smaller circle, r = 7 cm

Angle made by sectors of both concentric circles = 30°

Area of the larger sector = \(\dfrac{30°}{360°}
\)×πR^{2 }cm^{2}

= \(\dfrac{1}{12}\times \dfrac{22}{7}×21^2
\)^{ }cm^{2}

= \(\dfrac{231}{2}
\)cm^{2}

Area of the smaller circle = (\( \dfrac{30°}{360°}
\))×πr^{2 }cm^{2}

= \( \dfrac{1}{12}\times \dfrac{22}{7}×7^2\)^{ }cm^{2}

=\( \dfrac{77}{6}\) cm^{2}

Area of the shaded region = (\( \dfrac{231}{2}\)) – (\( \dfrac{77}{6}\)) cm^{2}

= \( \dfrac{616}{6}\) cm^{2} = \( \dfrac{308}{3}\)cm^{2}

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

A path of width 3.5 m runs around a semicircular grassy plot whose perimeter is 72 m. Find the area of the path.