Area of a Circle Math Example 3

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

hard

A circular garden has an area of

154

m². Find the radius of the garden. Use

\pi \approx \frac{22}{7}

1
Start with $A = \pi r^2$ and solve for $r$ : $r^2 = \frac{A}{\pi}$ .
2
Substitute: $r^2 = \frac{154}{\frac{22}{7}} = 154 \times \frac{7}{22} = \frac{1078}{22} = 49$ .
3
Take the square root: $r = 7$ m.

Answer

r = 7 \text{ m}

Solving for the radius from a known area requires dividing by

\pi

and taking the square root. Using

\pi \approx \frac{22}{7}

simplifies the arithmetic when the numbers work out neatly.

About Area of a Circle

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

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

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

A circular pond has radius [formula] m. A path around it extends the outer radius to [formula] m. Fi