Question

Circular foot path of width 2 m is constructed at the rate of ₹ 20 per m² around a circular path of radius 1500 m. Find the total cost of construction of the foot path.[ Take π= 3.14]
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

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=  (1500+2) m= 1502 m.

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

Area of the footpath =πR²-πr²

= π(R²-r²)

= 3.14(1502² - 1500²

= 3.14(1502+1500)(1502-1500)

= 3.14(3002)(2)

= 3.14(6004)

= 18852.56 m²

Total cost of construction of the footpath @ ₹ 20 per m²= 20 ×18852.56= ₹ 377051.2

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

HOPE THIS WILL HELP YOU....

Answer 2

Answer:

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=  (1500+2) m= 1502 m.

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

Area of the footpath =πR²-πr²

= π(R²-r²)

= 3.14(1502² - 1500²

= 3.14(1502+1500)(1502-1500)

= 3.14(3002)(2)

= 3.14(6004)

= 18852.56 m²

Total cost of construction of the footpath @ ₹ 20 per m²= 20 ×18852.56= ₹ 377051.2

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

HOPE THIS WILL HELP YOU....

Step-by-step explanation: