Question

Q5 If the perimeter of a sector of a circle of radius 6.4cm is 30cm ,then find the
area of corresponding sector​

Answer 1

Answer:

12.8 cm

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

sector is "55.04cm255.04cm^{2}55.04cm

2

".

Step-by-step explanation:

Given,

Radius(r) = 6.4 cm and perimeter of a sector of a circle = 30 cm

To find, the area of corresponding sector = ?

∴ Arc length of sector = Perimeter - 2r

= 30 cm - 2 × 6.4 cm = 17.2 cm

∴ θ=ArclengthRadius\theta =\dfrac{Arc length}{Radius}θ=

Radius

Arclength

=17.26.4=2.6875\dfrac{17.2}{6.4} =2.6875

6.4

17.2

=2.6875

Area of sector = πr2\pi r^{2}πr

2

=π6.42=4096πcm2\pi 6.4^{2}=4096 \pi cm^{2}π6.4

2

=4096πcm

2

Area of sector = θ2π×areaofcircle\dfrac{\theta}{2\pi } \times area of circle

2π

θ

×areaofcircle

=2.68752π×40.96π\dfrac{2.6875}{2\pi } \times40.96 \pi

2π

2.6875

×40.96π

= 55.04cm2cm^{2}cm

2

Hence, the area of corresponding sector is 55.04cm255.04cm^{2}55.04cm

2

.