(A) The length of an arc subtending an angle $\theta$ at the centre is given by $L = \frac{\theta}{360^{\circ}} \times 2\pi r$.The circumference of th

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(A) The length of an arc subtending an angle $\theta$ at the centre is given by $L = \frac{\theta}{360^{\circ}} \times 2\pi r$.The circumference of the circle is $C = 2\pi r$.Therefore,the ratio of the length of the minor arc $\widehat{ACB}$ to the circumference is $\frac{L}{C} = \frac{(\frac{\theta}{360^{\circ}}) \times 2\pi r}{2\pi r} = \frac{\theta}{360^{\circ}}$.Given $\theta = 72^{\circ}$,the ratio is $\frac{72^{\circ}}{360^{\circ}} = \frac{1}{5}$.Thus,the ratio is $1:5$.

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

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In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

A
$1:5$
B
$1:6$
C
$1:8$
D
$1:9$

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Mix Examples - Areas Related to Circles

In a circle with radius $10 \, cm$,the area of a minor sector is $75 \, cm^2$. Then,the length of the arc of that sector is $\ldots \, cm$.

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Four circular cardboard pieces of radii $7 \, cm$ are placed on a paper in such a way that each piece touches the other two pieces. Find the area of the portion enclosed between these pieces (in $cm^2$).

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As shown in the diagram,the side length of square $ABCD$ is $35 \, cm$. Two semicircles are drawn on its sides $\overline{AB}$ and $\overline{CD}$ as diameters. Find the area of the shaded region in $cm^2$.

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The length of the minute hand of a clock is $14\, cm$. The area of the region swept by it in $10$ minutes is $\ldots \ldots \ldots \, cm^2$.

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The circumference of a circle is $251.2 \, cm$. Find its diameter. $(\pi = 3.14)$ (in $cm$)

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In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

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In a circle with radius $10 \, cm$,the area of a minor sector is $75 \, cm^2$. Then,the length of the arc of that sector is $\ldots \, cm$.

Four circular cardboard pieces of radii $7 \, cm$ are placed on a paper in such a way that each piece touches the other two pieces. Find the area of the portion enclosed between these pieces (in $cm^2$).

As shown in the diagram,the side length of square $ABCD$ is $35 \, cm$. Two semicircles are drawn on its sides $\overline{AB}$ and $\overline{CD}$ as diameters. Find the area of the shaded region in $cm^2$.

The length of the minute hand of a clock is $14\, cm$. The area of the region swept by it in $10$ minutes is $\ldots \ldots \ldots \, cm^2$.

The circumference of a circle is $251.2 \, cm$. Find its diameter. $(\pi = 3.14)$ (in $cm$)

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