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JAMB Mathematics 2020 Paper

Question : 14

Total: 40

^{\circ}

. Calculate the perimeter of the sector.

Solution:

Concept:

The perimeter of a sector is the total length of its boundary, formed by the arc and two radii.

Explanation:

Given radius

r = 10.5

cm and sector angle

\theta = 48^\circ

First, find the arc length

L

using the formula

L = \frac{\theta}{360^\circ} \times 2\pi r

Substitute the values:

L = \frac{48}{360} \times 2 \times \frac{22}{7} \times 10.5

Simplify

\frac{48}{360} = \frac{2}{15}

and

10.5 = \frac{21}{2}

L = \frac{2}{15} \times 2 \times \frac{22}{7} \times \frac{21}{2}

This simplifies to

L = 8.8

cm.

Perimeter of sector

= L + 2r

Perimeter

= 8.8 + 2(10.5) = 8.8 + 21

Perimeter

= 29.8

cm.

Answer:

The perimeter of the sector is

29.8

cm.

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