Question

A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Find the approximate area of the path in square meters.

​

Answer 1

Explanation:

Area of the path = Area of the outer circle – Area of the inner circle = ∏{4/2 + 25/100}2 – ∏[4/2]2

= ∏[2.252 – 22] = ∏(0.25)(4.25) { (a2 – b2 = (a – b)(a + b) }

= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m

Answer 2

Answer:

• Area of path made = 3.34 m²

Explanation:

• Width of the path to be made around the circular garden = 25 cm = (25/100) m = 0.25 m
• The Diameter of the Circular garden, d = 4 m

We need to find the approximate area of the Path in square metres.

So,

Since the diameter of Circular garden is = 4 m

therefore, the radius of Circular garden, r = 2 m

Hence,

→ Area of circular ground will be, A₁ = π r²

→ A₁ = π ( 2 )² = 4 π  m²

Now,

When path of width 0.25 m will be made,

then new radius of Circular garden will be, R = 2 + 0.25 m = 2.25 m

Hence,

→ Area of circular garden along with path, A₂ = π R²

→ A₂ = π (2.25)² = 5.0625 π  m²

So,

→ Area of path = A₂ - A₁

→ Area of path = (5.0625 π) - ( 4 π )

→ Area of path = 1.0625  π

→ Area of path = 1.0625  ×  22/7

→ Area of path = 3.34  m²    [Approx.]

Therefore,

• Area of path made around the circular garden would be 3.34 m² approximately.