(A) Given: Radius $r = 8.4 \, cm$,Central angle $\theta = 60^{\circ}$.Area of minor sector = $\frac{\theta}{360^{\circ}} \times \pi r^2 = \frac{60}{36

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(A) Given: Radius $r = 8.4 \, cm$,Central angle $\theta = 60^{\circ}$.Area of minor sector = $\frac{\theta}{360^{\circ}} \times \pi r^2 = \frac{60}{360} \times \frac{22}{7} \times 8.4 \times 8.4 = \frac{1}{6} \times 22 \times 1.2 \times 8.4 = 36.96 \, cm^2$.Area of circle = $\pi r^2 = \frac{22}{7} \times 8.4 \times 8.4 = 221.76 \, cm^2$.Area of major sector = Area of circle - Area of minor sector = $221.76 - 36.96 = 184.8 \, cm^2$.

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

Easy

In a circle with radius $8.4 \, cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to this arc.

A
$36.96 \, cm^2, 184.8 \, cm^2$
B
$36.96 \, cm^2, 190.5 \, cm^2$
C
$38.50 \, cm^2, 184.8 \, cm^2$
D
$36.96 \, cm^2, 221.76 \, cm^2$

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Areas Related to Circles

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Mix Examples - Areas Related to Circles

Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?

Easy

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Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$ Part $II$

$1.$ Formula to find the length of a minor arc $a.$ $C=2\pi r$

$2.$ Formula to find the area of a minor sector $b.$ $A=\pi r^{2}$

$3.$ Formula to find the area of a circle $c.$ $l=\frac{\pi r \theta}{180}$

$4.$ Formula to find the circumference of a circle $d.$ $A=\frac{\pi r^{2} \theta}{360}$

Medium

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The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.

Easy

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In a circle with radius $20 \,cm$,the measures of the angle subtended at the centre for two distinct sectors are $15^{\circ}$ and $90^{\circ}$. Then,the ratio of the areas of those sectors is $\ldots \ldots \ldots$.

Medium

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As shown in the diagram, rectangle $ABCD$ is a metal sheet in which $CD = 20 \, cm$ and $BC = 14 \, cm$. From it, a semicircle with diameter $\overline{BC}$ and a sector with centre $A$ and radius $AD$ is cut off. Find the area of the remaining sheet in $cm^2$.

Medium

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Part $I$	Part $II$
$1.$ Formula to find the length of a minor arc	$a.$ $C=2\pi r$
$2.$ Formula to find the area of a minor sector	$b.$ $A=\pi r^{2}$
$3.$ Formula to find the area of a circle	$c.$ $l=\frac{\pi r \theta}{180}$
$4.$ Formula to find the circumference of a circle	$d.$ $A=\frac{\pi r^{2} \theta}{360}$

In a circle with radius $8.4 \, cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to this arc.

Similar Questions

Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?

The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.

In a circle with radius $20 \,cm$,the measures of the angle subtended at the centre for two distinct sectors are $15^{\circ}$ and $90^{\circ}$. Then,the ratio of the areas of those sectors is $\ldots \ldots \ldots$.

As shown in the diagram, rectangle $ABCD$ is a metal sheet in which $CD = 20 \, cm$ and $BC = 14 \, cm$. From it, a semicircle with diameter $\overline{BC}$ and a sector with centre $A$ and radius $AD$ is cut off. Find the area of the remaining sheet in $cm^2$.

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