Question

Circular footpath of width 2 m is constructed at the rate of Rs. 20 per square meter, around a circular park of radius 1500 m. Find the total cost of construction of the foot path.(Take π=3.14 )

Answer 1

FIGURE IS IN THE ATTACHMENT

SOLUTION:
Given:
Radius of  the park i.e inner radius of the park( r )= 1500m.
Width of the footpath around the park= 2 m
Let R be the outer radius of the park including the footpath.

R = inner radius of the park( r ) + Width of the footpath
R=  (1500+2) m= 1502 m.

Area of the footpath = Area of the circular path including footpath - Area of the circular path excluding footpath

Area of the footpath =πR²-πr²
Area of the footpath= π(R²-r²)
= 3.14(1502² - 1500²)
= 3.14(1502+1500)(1502-1500)

[a² - b² = (a+b)(a-b)]
= 3.14(3002)(2)
= 3.14(6004)
= 18852.56 m²

Rate of construction of the footpath =  ₹ 20 per m²
Total cost of construction of the footpath at the rate of  ₹ 20 per m²= 20 ×18852.56= ₹ 377051.2

Hence, the Total cost of construction of the footpath is  ₹ 377051.2.

HOPE THIS WILL HELP YOU....

Answer 2

hiii!!!

here's ur answer...

given the radius of the circular park = 1500m

area of the circular park = πr²

= 3.14 × 1500 × 1500

= 7065000m²

ATQ,

the 2m wide path is constructed all around the path, so the radius of the park along with the path will be = 1500 + 2 = 1502m

area of the park along with the path = πr²

= 3.14 × 1502 × 1502

= 7,083,852.56m²

therefore area of the path = 7,083,852.56 - 7065000

= 18,852.56m²

total cost of construction of the footpath at the rate of ₹20 per m² = 18,852.56 × 20

= ₹377,051.2

hope this helps..!!