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The area of a sector of a circle of radius 5
cm, formed by an arc of length 3.5 cm is
(a) 8 cm?
(b) 8.75 cm?
(c) 9.5 cm?
(d) 7.9 cm?
​

Sagot :

Answer:

A = 8.75 cm²

Step-by-step explanation:

Given that,

Radius, r = 5 cm

The arc length, l = 3.5 cm

We need to find the area of a sector. Let [tex]\theta[/tex] be the angle. So,

[tex]\theta=\dfrac{l}{r}\\\\\theta=\dfrac{3.5}{5}\\\\\theta=0.7\ rad[/tex]

The formula for the area of sector when [tex]\theta[/tex] is in radian is  given by :

[tex]A=\dfrac{1}{2}\times \theta r^2\\\\A=\dfrac{1}{2}\times 0.7\times 5^2\\\\A=8.75\ cm^2[/tex]

So, the area of the sector is 8.75 cm².

Answer: (b)

Step-by-step explanation:

Given

the radius of circle r=5 cm

arc length  [tex]l=3.5\ cm[/tex]

Arc length is also given by

[tex]l=\dfrac{\theta }{360^{\circ}}\times 2\pi r[/tex]

[tex]\Rightarrow 3.5=\dfrac{\theta }{360^{\circ}}\times 2\pi \times 5\\\\\Rightarrow \theta =40.10^{\circ}[/tex]

Area of the sector is given by

[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\times \pi r^2\\\\\Rightarrow A=\dfrac{40.101^{\circ}}{360^{\circ}}\times 3.142\times 5^2\\\\\Rightarrow A=8.749\approx 8.75\ cm^2[/tex]

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