Question

A circular pond has a radius of 70m. A 7m wide footpath runs around it. Find the area of the footpath. What will be the cost of levelling the footpath at Rs 15 per sq m?

Answer 1

GIVEN :-

• Radius of circular pond ( r ) = 70 m.
• Width of footpath ( w ) = 7 m.

TO FIND :-

• The area of footpath.

SOLUTION :-

Let the radius of circular pond be "r" and the radius of outer circle ( bigger circle ) be "R".

➳ R = r + w

➳ R = 70m + 7m

➳ R = 77m.

Now,

➳ Area of footpath = πR² - πr²

➳ Area of footpath = 22/7 × (77)² - 22/7 × (70)²

➳ Area of footpath = 22 × 77 × 11 - 22 × 70 × 10

➳ Area of footpath = 18634 - 15400

➳ Area of footpath = 3234m²

Now,

➳ Total cost of levelling = Area × Rate

➳ Total cost of levelling = 3234 × 15

➳ Total cost of levelling = Rs. 48510

Hence Total cost of levelling the footpath = Rs. 48510.

Answer 2

Answer:

$\huge\sf\red{Question}$

A circular pond has a radius of 70m. A 7m wide footpath runs around it. Find the area of the footpath. What will be the cost of levelling the footpath at Rs 15 per sq m?

$\huge\sf\red{Answer}$

given :

• Radius of the circular pond = 70 m

• Width of the foot path that runs around it = 7 m

Let the radius of the outer circle formed by the circular path be x

Therefore , radius ( x ) of the outer circle :

x = radius of circular pond + width of the circular path .

x = 70 m + 7 m

x = 77 m

• Therefore radius of the outer circle = 77 m

Area of the footpath = Area of outer circle - Area of circular pond

➡️ πx² - πr²

➡️ 22/7 × 77 × 77 - 22/7 × 70 × 70

➡️ 22 × 11 × 77 - 22 × 10 × 70

➡️ 18634 - 15400

➡️ 3234

Cost of levelling = 3234 × 15

➡ Rs .️ 48510