Question : What will be the area of the semi-circle of perimeter 3.6 metres?
Option 1: 1.54 m2
Option 2: 1.76 m2
Option 3: 1.10 m2
Option 4: 0.77 m2
Correct Answer: 0.77 m 2
Solution :
Given: The perimeter of the semi-circle is 3.6 metres.
Let the radius of the semi-circle be $r$.
According to the question,
$\pi r + 2r=3.6$
⇒ $r(\pi+2)=3.6$
⇒ $r(\frac{22}{7}+2)=3.6$
⇒ $r(\frac{36}{7})=3.6$
⇒ $r=3.6×\frac{7}{36}$
⇒ $r=\frac{7}{10}$ metres
So, the area of the semi-circle = $\frac{1}{2}\pi r^2$
= $\frac{1}{2}×\frac{22}{7}×\frac{7}{10}×\frac{7}{10}$
= 0.77 m
2
Hence, the correct answer is 0.77 m
2
.
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