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5 votes
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?


2 Answers

5 votes

Answer: (b)

Explanation:

Given

the radius of circle r=5 cm

arc length
l=3.5\ cm

Arc length is also given by


l=(\theta )/(360^(\circ))* 2\pi r


\Rightarrow 3.5=(\theta )/(360^(\circ))* 2\pi * 5\\\\\Rightarrow \theta =40.10^(\circ)

Area of the sector is given by


\Rightarrow A=(\theta )/(360^(\circ))* \pi r^2\\\\\Rightarrow A=(40.101^(\circ))/(360^(\circ))* 3.142* 5^2\\\\\Rightarrow A=8.749\approx 8.75\ cm^2

User Thobe
by
8.4k points
1 vote

Answer:

A = 8.75 cm²

Explanation:

Given that,

Radius, r = 5 cm

The arc length, l = 3.5 cm

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


\theta=(l)/(r)\\\\\theta=(3.5)/(5)\\\\\theta=0.7\ rad

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


A=(1)/(2)* \theta r^2\\\\A=(1)/(2)* 0.7* 5^2\\\\A=8.75\ cm^2

So, the area of the sector is 8.75 cm².

User Xenish
by
8.2k points

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