QUESTION 4
Easy
Find the perimeter of a sector(i.e., the curved portion as well as the two straight portions) of a circle of radius 14 cm and sector angle 75°.
SOLUTION
1
Write down what is given
Given,
\(r = 14\,cm\)
\(θ = 75°\)
\(r = 14\,cm\)
\(θ = 75°\)
2
Find the arc length
\(\begin{aligned} Arc\,Length, \,L &= \frac{75}{300} × 2 × \frac{22}{7} × 14 \\ &= \frac{75}{360} × 88 \\ &= \frac{5}{24} × 88 \\ &= \frac{440}{24} \\ &= \frac{55}{3} \\ &= 18.33\,cm \end{aligned}\)
3
Find the perimeter
\(Perimeter\, = \,Arc\, length\, +\, 2r\)
\(\begin{aligned} Perimeter &= 18.33 + 2(14) \\ &= 18.33 + 28 \\ &= 46.33\,cm \end{aligned}\)
The perimeter of the sector is 46.33 cm.
\(\begin{aligned} Perimeter &= 18.33 + 2(14) \\ &= 18.33 + 28 \\ &= 46.33\,cm \end{aligned}\)
The perimeter of the sector is 46.33 cm.
🏆
Final Answer : The perimeter of the sector is 46.33 cm.
Concept Note
The perimeter of a sector consists of:
(i) the arc length
(ii) two radii
Perimeter = Arc length + 2r, where
Arc length \(= \frac{θ}{360} × 2πr\)