(C) The area of a circle is given by $A = \pi r^{2}$.The area of a minor sector subtending an angle $\theta$ at the centre is given by the formula $\f

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$\pi r^{2} - \frac{\pi r^{2} \theta}{360}$

(C) The area of a circle is given by $A = \pi r^{2}$.The area of a minor sector subtending an angle $\theta$ at the centre is given by the formula $\frac{\theta}{360} \times \pi r^{2}$.The major sector is the remaining part of the circle.Therefore,the area of the major sector = (Area of the circle) - (Area of the minor sector).Area of major sector = $\pi r^{2} - \frac{\pi r^{2} \theta}{360}$.

Class 10 Mathematics Areas Related to Circles Mix Examples - Areas Related to Circles

Medium

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

A
$\frac{\pi r \theta}{180}$
B
$2 \pi r - \frac{\pi r \theta}{180}$
C
$\pi r^{2} - \frac{\pi r^{2} \theta}{360}$
D
$\frac{\pi r^{2} \theta}{360}$

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Areas Related to Circles

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Mix Examples - Areas Related to Circles

If the area of a circle is $154 \, cm^2$,then its perimeter (circumference) is (in $cm$):

Easy

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The circumference of a circle is $88 \, cm$. The length of each side of a square inscribed in that circle is $\ldots \ldots \ldots \, cm$.

Medium

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The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

Difficult

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With respect to the given diagram,which of the following correctly matches the information in Part $I$ and Part $II$?

Part $I$ Part $II$

$1. \overline{OA} \cup \overline{OB} \cup \widehat{APB}$ $a. \text{Major sector}$

$2. \overline{AB} \cup \widehat{AQB}$ $b. \text{Minor segment}$

$3. \overline{AB} \cup \widehat{APB}$ $c. \text{Minor sector}$

$4. \overline{OA} \cup \overline{OB} \cup \widehat{AQB}$ $d. \text{Major segment}$

Part $I$	Part $II$
$1. \overline{OA} \cup \overline{OB} \cup \widehat{APB}$	$a. \text{Major sector}$
$2. \overline{AB} \cup \widehat{AQB}$	$b. \text{Minor segment}$
$3. \overline{AB} \cup \widehat{APB}$	$c. \text{Minor sector}$
$4. \overline{OA} \cup \overline{OB} \cup \widehat{AQB}$	$d. \text{Major segment}$

Medium

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The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots \,cm^2$.

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In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

Similar Questions

If the area of a circle is $154 \, cm^2$,then its perimeter (circumference) is (in $cm$):

The circumference of a circle is $88 \, cm$. The length of each side of a square inscribed in that circle is $\ldots \ldots \ldots \, cm$.

The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots \,cm^2$.

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