The diagram shows a sector of a circle radius $11 \mathrm{~cm}$.
Show that the perimeter of the sector is greater than $47.5 \mathrm{~cm}$.
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Answer

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Answer

The final answer is 22+(11x*pi)/180 > 47.5

Steps

Step 1 ：Assume the angle of the sector is x degrees

Step 2 ：Calculate the arc length: (11x*pi)/180

Step 3 ：Calculate the perimeter: 22+(11x*pi)/180

Step 4 ：Show that 22+(11x*pi)/180 > 47.5

Step 5 ：Subtract 22 from both sides: (11x*pi)/180 > 25.5

Step 6 ：Multiply both sides by 180/(11*pi): x > 25.5*(180/(11*pi))

Step 7 ：Calculate the value of x: x > 132.3 degrees

Step 8 ：Since the angle of the sector is greater than 132.3 degrees, the perimeter of the sector is greater than 47.5 cm

Step 9 ：The final answer is 22+(11x*pi)/180 > 47.5