The area of a circular garden is 55.44 m². How long wire is needed for fencing the garden ?

1. 21.4 m

2. 22.4 m

3. 24.6 m

4. 26.4 m

Given,

Area of circle = 55.44 m².

By formula,

$\text{Area of circle} = πr^2 \\[1em] \Rightarrow 55.44 = πr^2 \\[1em] \Rightarrow \dfrac{22}{7} \times r^2 = 55.44 \\[1em] \Rightarrow r^2 = \dfrac{55.44 × 7}{22} \\[1em] \Rightarrow r^2 = 17.64 \\[1em] \Rightarrow r = \sqrt{17.64} \\[1em] \Rightarrow r = 4.2 \text{ m}.$

Wire length = Circumference of the circle

= 2πr

= 2 × $\dfrac{22}{7}$ × 4.2

= 26.4 m.

Hence, option 4 is the correct option.