A park is in the shape of a circle of diameter 7 m. It is surrounded b

1.	A park is in the shape of a circle of diameter 7 m. It is surrounded by a path of width 0.7 m. Find the expenditure of cementing the path at the rate of ₹ 110 per sq.m.
Answer» Diameter of park = 7 m so, radius of park = r₁ = 3.5 m Width of park = 0.7 m Bigger radius of park = r₂ = 0.7 + 3.4 = 4.2 m Now, Area of path = area of bigger circle -area of smaller circle = Pi r₂² – Pi r₁² = Pi(r₂² – r₁²) = 22/7 (4.2²– 3.5 ²) = 22/7(17.64 – 12.25) =16.94 m² Also, Cost of expenditure = rate × area = 110 × 16.94 = 1864.40 Cost of Expenditure of cementing the path is ₹ 1864.40.

A park is in the shape of a circle of diameter 7 m. It is surrounded by a path of width 0.7 m. Find the expenditure of cementing the path at the rate of ₹ 110 per sq.m.

Answer»

Diameter of park = 7 m

so, radius of park = r₁ = 3.5 m

Width of park = 0.7 m

Bigger radius of park = r₂ = 0.7 + 3.4 = 4.2 m

Now, Area of path = area of bigger circle -area of smaller circle

= Pi r₂² – Pi r₁²

= Pi(r₂² – r₁²)

= 22/7 (4.2²– 3.5 ²)

= 22/7(17.64 – 12.25)

=16.94 m²

Also,

Cost of expenditure = rate × area

= 110 × 16.94

= 1864.40

Cost of Expenditure of cementing the path is ₹ 1864.40.