Question

A paved walkway around a garden has an outer diameter of 80 ft and an inner diameter of 40 ft. A diagram is shown below.

What is the approximate area of the paved walkway?

Answer 1

The area of the paved walkway is found by calculating the area of the outer circle with a diameter of 80 ft and subtracting the area of the inner circle with a diameter of 40 ft. The approximate area of the walkway is 3768 square feet.

Step-by-step explanation:

To calculate the area of the paved walkway around a garden, with an outer diameter of 80 ft and an inner diameter of 40 ft, we first have to consider the area of the large circle and then subtract the area of the smaller circle from it. The formula for the area of a circle is A = πr², where A is the area and r is the radius of the circle.

The radius of the outer circle is 40 ft (half of the outer diameter), and the radius of the inner circle is 20 ft (half of the inner diameter). Therefore, the area of the outer circle is A_outer = π × (40 ft)² and the area of the inner circle is A_inner = π × (20 ft)². To find the area of the walkway, we subtract the inner area from the outer area: Area of walkway = A_outer - A_inner.

Using π ≈ 3.14, the calculation would be:

• A_outer ≈ 3.14 × (40 ft)² ≈ 3.14 × 1600 ft² ≈ 5024 ft²
• A_inner ≈ 3.14 × (20 ft)² ≈ 3.14 × 400 ft² ≈ 1256 ft²
• Area of walkway ≈ 5024 ft² - 1256 ft² ≈ 3768 ft²

Therefore, the approximate area of the paved walkway is 3768 square feet.

Answer 2

Given:

• Outer diameter = D = 80 ft
• Inner diameter = d = 40 ft

So,

Outer radius = R = D/2

=> R = (80 ft)/2

=> R = 40 ft

Inner radius = r = d/2

=> r = (40 ft)/2

=> r = 20 ft

Area of paved pathway = πR² - πr²

= π(R² - r²)

= π(R + r)(R - r)

= π(40 + 20)(40 - 20) ft²

= π(60)(20) ft²

= 3.14 * 1200 ft²

= 3768 ft²