Question

A circular garden with radius 42 m is surrounded from
outside by a path of 3.5 m wide. Find the cost to pave the
stones on the path at the rate of Rs. 20 per m2.
(Ans: Rs. 19250)​

Answer 1

Given :

Radius of inner circle = 42m

• A circular garden is surrounded from outside by a path of 3.5 m wide

Radius of outer circle = 42 + 3.5 = 45.5 m

• The rate of pave the stones on the path = Rs20

To find :

The total cost to pave the stones on the path.

Solution :

★ Area of outer circle - Area of inner circle

Consider inner radius be 'r' and outer radius be 'R'

→ πR² - πr²

• Take π as a common

→ π(R² - r²)

• Apply identity
• a² - b² = (a + b)(a - b)

→ π(R + r)(R - r)

• Substitute the values of radius

→ π(45.5 + 42)(45.5 - 42)

→ π × 87.5 × 3.5

→ 22/7 × 87.5 × 3.5

→ 22 × 87.5 × 0.5

→ 962.5 m²

•°• The area of paving stones on the path is 962.5m²

$\:$ ━━━━━━━━━━━━━━━━━━━━━━━━

★ The rate of pave the stones on the path = Rs20

→ The total cost to pave the stones on the path

→ 962.5 × 20

→ Rs.19250

•°• The total cost to pave the stones is Rs.19250

$\:$ ━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

Given :-

Radius = 42 m

Path = 3.5 m

To Find :-

Cost

Solution :-

When path built then the new radius become = 42 + 3.5 = 45.5 m

Now

Cost = Area × Rate

Let the old radius be r and new radius be R

Area of the garden

π(R² - r²)

22/7(45.5² - 42²)

22/7 × (2070.25 - 1764)

22/7 × 306.25

962.5 m

Now

Cost = Area × Rate

Cost = 962.5 × 20

Cost = 19250