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Q5(ii):
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (ii) area of the sector formed by the arc (Unless stated otherwise, use $\pi = \frac{22}{7}$)

Solution :

Given:

Radius of the circle ($r$) = $21\text{ cm}$

Angle subtended by the arc at the centre ($\theta$) = $60^\circ$

Value of $\pi$ = $\frac{22}{7}$

To Find:

Area of the sector formed by the arc.

60° r = 21 cm O

Step 1: Stating the Formula

The area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees) is given by the formula:

$\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2$

[Where $\theta$ is the angle subtended at the centre and $r$ is the radius of the circle.]

Step 2: Substituting the Given Values

Substitute $\theta = 60^\circ$, $r = 21\text{ cm}$, and $\pi = \frac{22}{7}$ into the formula:

$\text{Area} = \frac{60}{360} \times \frac{22}{7} \times (21)^2$

Step 3: Simplifying the Expression

First, simplify the fraction $\frac{60}{360}$:

$\frac{60}{360} = \frac{1}{6}$

Now, expand $(21)^2$:

$(21)^2 = 21 \times 21 = 441$

Substitute these back into the equation:

$\text{Area} = \frac{1}{6} \times \frac{22}{7} \times 441$

Step 4: Performing the Arithmetic Calculation

Divide $441$ by $7$:

$441 \div 7 = 63$

Now the expression is:

$\text{Area} = \frac{1}{6} \times 22 \times 63$

Simplify $\frac{63}{6}$ by dividing both by $3$:

$\frac{63}{6} = \frac{21}{2} = 10.5$

Now multiply the remaining terms:

$\text{Area} = 22 \times 10.5$

$22 \times 10.5 = 231$

Final Answer:

The area of the sector formed by the arc is $231\text{ cm}^2$.


More Questions from Class 10 Mathematics Areas Related to Circles EXERCISE 11.1


CBSE Solutions for Class 10 Mathematics Areas Related to Circles


Chapters in CBSE - Class 10 Mathematics


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