Area of circular pathway

Area of circular pathway Concentric circles Circles drawn in a plane with a common centre and different radius are called concentric circles Area of circular pathway A track of uniform width is laid around a circular park for walking purpose. What is the area of this track ? Area of the track is the area bounded between two concentric circles. O is the common centre of the two circles. Let the radius of the outer circle be R and inner circle be r.

The shaded portion is known as the circular ring or the circular pathway. i.e. a circular pathway is the portion bounded between two concentric circles. width of the pathway, w = R – r units i.e., w = R – r & R = w + r units r = R – w units. Area of the circular pathway = Area of outer circle – Area of inner circle = πR2 – πr2 sq. units = π (R2 – r2) sq. units ∴ Area of the circular pathway = π (R + r) (R – r) sq. units

larger circle is 14 cm and the smaller circle is 7 cm. Example 1:- The adjoining figure shows two concentric circles. The radius of the larger circle is 14 cm and the smaller circle is 7 cm. Find the area of the circular pathway. Solution Given: Radius of large circle(R) = 14 m Radius of small circle (r) = 7 m To Find: The area of the circular pathway. We know that Area of the circular path = π(R + r)(R – r) 14cm 7cm 3 = 22 x 3 x 7 = 462 Ans:- Area of the circular path is 462 cm2

Example 2:- A uniform circular path of width 2 m is laid out side a circular park of radius 50 m. Find the cost of levelling the path at the rate of Rs 5 per m2 (Take π = 3.14) Solution Given: r = 50 m, w = 2 m, We know that R = r + w =50 + 2 = 52 m To Find:- Cost of levelling the path Step1:- Find the area of circular path Area of the circular path = π(R + r)(R – r) = 3.14 x (52 + 50) (52 – 50) (Take π = 3.14) = 3.14 x 102 x 2 = 640.56 m2 Step2:- Find the cost of levelling the circular path The cost of levelling the path of area 1 sq m = Rs 5 The cost of levelling the path of 640.56 m2 = 5 x 640.56= 3202.80 Ans:- The cost of levelling the path = Rs 3202.80

circle is 8 m, find the radius of the inner circle. Example 3:- The area of the circular pathway is 88 m2. If the radius of the outer circle is 8 m, find the radius of the inner circle. Given:- Outer circle radius(R)=8m, area of the circular pathway=88 m2 To Find:- radius of inner circle To find radius of inner circle we need to Step1:- Find Area of outer circle Step2:- Find Area of inner circle Step3:- Find radius of inner circle We know that Area of outer circle = πr2 Area of outer circle

Step2:- Find Area of inner circle Area of the circular pathway = Area of outer circle – Area of inner circle ∴ Area of inner circle = Area of circular pathway – Area of outer circle Step3:- Find radius of inner circle We know that Area of inner circle = πr2 36 r x r =36 Since 6 x 6 = 36, ∴ r= 6 Ans:-The radius of inner circle is 6m

Try these A circular well has radius 2 m. If a platform of uniform width of 1 m is laid around it, find the area of the platform . (Take π = 3.14) A uniform circular path of width 1.5 m is laid outside a circular park of radius 35m. Find the cost of levelling the path at the rate of Rs 5 per m2. (Take π = 3.14)