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The angle of a sector of a circle of radius 10.5cm is 48°, Calculate the perimeter of the sector

A. 8.8cm

B. 25.4cm

C. 25.6cm

D. 29.8cm

QUICK ANSWER…

D

DETAILS…

If the angle of a sector of a circle of radius 10.5cm is 48°, the perimeter of the sector will be = 29.7979cm

Perimeter of a sector = length of arc + 2r

Where r = radius of the circle.

Now, lets find the length of arc of the sector.

Length of arc = θ/360 × 2πr

Length of arc = 48/360 × 2 × 3.142 × 10.5

Length of arc = 8.7979cm

Therefore, perimeter of the sector = 8.7979 + 2 × 10.5

perimeter of the sector = 8.7979 + 21 = 29.7979 = 29.8cm

Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is not correct.
3. C is incorrect.
4. D is the correct answer.

KEY-POINTS…

You may please note these/this:

• Perimeter of a sector of a circle = length of arc + 2r.
• Length of arc = θ/360 × 2πr.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 17 /