Question

Find the path area of circular shaped grassland of radius 42 m where width of the path is 7 m. around and outside the circle. Find the area of path and total cost of flooring, if the cost of flooring ₹ 150 per sq.m.

Answer 1

Radius of circular floor = 42 m 

Width around it = 7 m 

Radius of outer circle = 42 + 7 = 49 m 

Area of outside path = Area of outer circle – Area of inner circle 

Area of inner circle = πr² = \(\frac {22}7\) × 42 × 42 

Area of the outer circle = πr² = \(\frac {22}7\) × 49 × 49 

Area of floor = \(\frac {22}7\)(49 × 49 – 42× 42) 

= \(\frac {22}7\)(2401 – 1764) 

= \(\frac {22}7\)× 637 = 2002 m² 

∴ Cost of flooring at the rate of ₹ 150 per sq.m is 2002 × 150 = ₹ 300300