Question

The radius and length of arc of a sector are $10cm$and $15cm$respectively. Find its perimeter.

Answer 1

Hint: Perimeter of any arc can be calculated by adding sum of all its out lengths. So, the perimeter of a sector can be found by calculating the sum of its radius and length of arc and hence required solution of the given problem.

Complete step-by-step answer:
Given radius of the circle =$10\;cm$.
Length of an arc = $15\;cm$
We know that the perimeter of any curve is the total distance of the outer boundary of a given curve.
Hence, to find the perimeter of the sector. We will find the total out distance of the sector.

From the figure we see that the perimeter of a sector is the sum of three parts. Sum of two radius of circle and other length of arc of sector.
Therefore perimeter of sector is given as:
$
\Rightarrow 10 + 10 + 15 \\
   = 35\;cm \;
 $
Hence, from above we see that perimeter of a sector is $35\;cm.$
So, the correct answer is “35 cm”.

Note: Perimeter is the total outer distance that a body has. If there is any line joining in between curves it would not be a part of the perimeter. For perimeter we only add distance of only outer part of curve of given curve.