Question

Find the radius of a circle whose circumference is equal to the perimeter of a regular pentagon of side length $44.44$ cm.$(\pi =\frac{22}{7})$

• A. $35$ cm
• B. $36$ cm
• C. $35.3$ cm
• D. $35.35\text{cm}$

Answer 1

The correct option is D $35.35\text{cm}$

Firstly let us find out the perimeter of the regular pentagon.
$\text{perimeter}=5\times \text{(side length)}$
$\text{perimeter}=5\times 44.44\text{cm}$

Now, we know
$\text{circumference of circle}=2\pi r$
where $r=\text{radius of circle}$

Given: $\text{Circumference of the circle}\text{= Perimeter of the regular pentagon}$

$\therefore \text{Circumference of the circle}=5\times 44.44\text{cm}$
$\Rightarrow 5\times 44.44=2\pi r$
$\Rightarrow 5\times 44.44=2\times \frac{22}{7}r\Rightarrow r=\frac{5\times 44.44\times 7}{22\times 2}\Rightarrow r=5\times 1.01\times 7=35.35\text{cm}$

Hence, correct answer is option $\left(d\right)$.