MATHEMATICS

JAMB 2018 - Question 20

Mathematics 2018 JAMB Past Questions - Question 20: An arc of circle of radius 14cm subtends angle 300degree at the centre.Find the perimeter of the sector formed by the arc

An arc of circle of radius 14cm subtends angle 300degree at the centre.Find the perimeter of the sector formed by the arc
A:
B:
C:
D:
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Correct Answer

C

Explanation

The perimeter of the sector formed by the arc can be found using the formula:\[ \text{Perimeter} = \text{Length of the arc} + 2r \]First, let's find the length of the arc. The formula for the length of an arc is:\[ \text{Length of arc} = \frac{\text{angle}}{360^\circ} \times 2\pi r \]Substituting the given values:\[ \text{Length of arc} = \frac{300^\circ}{360^\circ} \times 2\pi \times 14 \]\[ \text{Length of arc} = \frac{5}{6} \times 28\pi \]\[ \text{Length of arc} = \frac{140\pi}{6} \]\[ \text{Length of arc} = \frac{70\pi}{3} \]Now, we can find the perimeter of the sector:\[ \text{Perimeter} = \frac{70\pi}{3} + 2 \times 14 \]\[ \text{Perimeter} = \frac{70\pi}{3} + 28 \]So, the perimeter of the sector formed by the arc is \( \frac{70\pi}{3} + 28 \) cm.

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