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

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.