Question

A circular path has to be constructed around a circular lawn. If the outer and inner circumferences of the path are 88 cm and 44 cm respectively, find the width and area of the path.

Answer 1

Outer circumference of the circular lawn = 88 cm

2πR = 88 cm

Inner circumference of the lawn 2πr = 44 cm

2πR – 2πr = 88 – 44

2 x \(\frac{22}{7}\) (R – r) = 44

(R – r) = \(\frac{44\times7}{2\times22}\)

Outer radius – Inner radius = 7 cm

∴ Width of the lawn = 7 cm

Also 2πR + 2πr = 88 + 44

2π(R + r) = 132

π(R + r) = \(\frac{132}{2}\) 

= 66 cm

Area of the path = πR² – πr² sq. units

= π(R + r) (R – r)

= 66 x 7 cm²

Area of the path = 462 cm²