Area of a Circle Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A circular pond has radius 66 m. A path around it extends the outer radius to 99 m. Find the area of the path.

Solution

  1. 1
    Find the area of the outer circle: Aouter=ฯ€(9)2=81ฯ€A_{\text{outer}} = \pi(9)^2 = 81\pi mยฒ.
  2. 2
    Find the area of the pond: Ainner=ฯ€(6)2=36ฯ€A_{\text{inner}} = \pi(6)^2 = 36\pi mยฒ.
  3. 3
    Subtract to get the path area: 81ฯ€โˆ’36ฯ€=45ฯ€81\pi - 36\pi = 45\pi mยฒ.

Answer

45ฯ€ย m245\pi \text{ m}^2
A path around a circle creates an annulus, which is the region between two concentric circles. Its area is the larger circle minus the smaller circle.

About Area of a Circle

The amount of space enclosed inside a circle, calculated as ฯ€\pi times the square of the radius.

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More Area of a Circle Examples

Example 1 easy

Find the area of a circle with radius [formula] cm. Leave your answer in terms of [formula].

Example 2 medium

Find the area of a semicircle with diameter [formula] cm. Give your answer to one decimal place.

Example 3 hard

A circular garden has an area of [formula] mยฒ. Find the radius of the garden. Use [formula].

โ† All Area of a Circle Examples Area of a Circle Concept