Question

the circumference of a circular flower bed is 132m find its area

Answer 1

$2\pi \times r = 132 \\ \\ 2 \times \frac{22}{7} \times r = 132 \\ \\ r = 132 \times 7 \div 44 = 21m \\ \\ area = \pi \times {r}^{2} = \frac{22}{7} \times 21 \times 21 = 22 \times 63 = 1386 {m}^{2}$


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Answer 2

Given:

The circumference of a circular flower bed = 132m

To Find:

The area of the flower bed

Solution:

We know that circumference of a circle = 2πr

⇒ 2πr = 132      -(1)

Here r is the radius of the flower bed

Let the area of the flower bed be A

So A = πr²     - (2)

Dividing equation 1 by 2,

$\frac{2\pi r}{\pi r^2} = \frac{132}{A}$

or 2 / r = 132 / A

Cross multiplying,

2 X A = 132 X r

or A = 66r      - (3)

From equation 1,

r = 132 / 2π

Substituting in equation 3,

A = 66 X 132 / 2π

= 66 X 66 / π

Taking π = 22 / 7

A = 66 X 66 X 7 / 22

= 21 X 22

= 462 m²

Hence, the area of the circular flower bed is 462 m².