(A) Yes, it is necessary that their areas be equal.Let the circumferences of two circles be $C_1$ and $C_2$, and their radii be $r_1$ and $r_2$ respec

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Yes, because their radii must be equal.

(A) Yes, it is necessary that their areas be equal.Let the circumferences of two circles be $C_1$ and $C_2$, and their radii be $r_1$ and $r_2$ respectively.Given that $C_1 = C_2$, we have $2\pi r_1 = 2\pi r_2$.Dividing both sides by $2\pi$, we get $r_1 = r_2$.The area of a circle is given by $A = \pi r^2$.Since $r_1 = r_2$, it follows that $\pi r_1^2 = \pi r_2^2$, which means $A_1 = A_2$.Therefore, if the circumferences of two circles are equal, their areas must also be equal.

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

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Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

A
Yes, because their radii must be equal.
B
No, because area depends on the square of the radius.
C
Yes, but only if the circles are in the same plane.
D
No, because circumference is independent of area.

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Areas Related to Circles

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Mix Examples - Areas Related to Circles

In a circle with radius $6 \, cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.

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The radius of a circular ground is $56\,m$. $A$ $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by the shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40/m^2$ (in ₹).

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In the figure,arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side $10 \, cm$ as centers to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D, E$ and $F$. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

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The area of a circle is $200 \, cm^{2}$. Then,the area of a minor sector of that circle can be $\ldots \ldots \ldots \, cm^{2}$.

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The length of a minor arc of $\odot(O, 7)$ can be $\ldots \ldots \ldots \ldots$ units.

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Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

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In a circle with radius $6 \, cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.

The radius of a circular ground is $56\,m$. $A$ $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by the shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40/m^2$ (in ₹).

In the figure,arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side $10 \, cm$ as centers to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D, E$ and $F$. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

The area of a circle is $200 \, cm^{2}$. Then,the area of a minor sector of that circle can be $\ldots \ldots \ldots \, cm^{2}$.

The length of a minor arc of $\odot(O, 7)$ can be $\ldots \ldots \ldots \ldots$ units.

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