Question

The length of an arc of a circle subtending an angle of measure 60° at the centre is 10 cm. Find the area and the circumference of the circle.

Answer 1

Answer:

theta=60°. r=10cm

theta/360×πr2

Step-by-step explanation:

=60/360×22/7×10×10

=1/6×22/7×100

=2200/42

=1100/21

Answer 2

Concept

The arc length formula is used to calculate a measure of  distance along the curve forming the arc (circle segment). Simply put, the distance  through the circular curve that makes up the arc is called the arc length. Note that the arc length is longer than the straight line distance between the endpoints.

The arc length formula in radians can be expressed as, arc length = θ × r, when θ is in radian. Arc Length = θ × (π/180) × r, ...(1) where θ is in degree, where,

L = Length of an Arc

θ = Central angle of Arc

r = Radius of the circle

Given

We have been given that length of an arc of a circle is 10 cm and the angle subtended by the arc is $60 \textdegree$ .

Find

We are asked to determine the area and circumference of the circle .

Solution

We need to find radius for area and circumference of the circle.

Putting $\theta=60\textdegree \ ,L=10cm$ in equation (1) , we get

$L=\theta\times\frac{\pi }{180} \times r\\\\10=60\times \frac{\pi }{180} \times r\\\\r=\frac{10\times180}{60\times\pi } \\\\r=\frac{30}{3.14}\\\\r=9.55$

Area of the circle $=\pi r^2$

                           $=3.14(9.55)^2\\=286.37cm^2$

Circumference of the circle $=2\pi r$

                                              $=2\times3.14\times9.55\\=59.974cm$

Therefore, the area and circumference of the circle are $286.37cm^2$and 59.974 cm respectively

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