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Area of a Circle

In the figure...

Question

In the figure, from the handkerchief from four corners, sectors P, Q, R and S each of $2 c m$ are cut, whose sum is $P + Q + R + S = A_{1}$ and a circle of diameter $4 c m$ from the centre is cut whose area is $A_{2}$ , then ______ is possible.

A_{1} \neq A_{2}

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A_{1} < A_{2}

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A_{1} > A_{2}

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A_{1} = A_{2}

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Solution

The correct option is A $A_{1} = A_{2}$
In the figure, from one handkerchief from four corners, sectors P, O, R and S of $2 c m$ are cut.
$∴ A_{1} = P + Q + R + S$
$= 4 (\frac{π r^{2}}{4})$ ..... (where $r = 2 c m$ )
$= π (2)^{2}$
$= 4 π c m^{2}$ ........(1)
The diameter of the circle lies on centre is $4$ cm.
$∴$ Its radius is $2 c m$
$∴$ $A_{2} = π r^{2}$ ...... (where $r = 2 c m$ )
$= π (2)^{2}$
$= 4 π (c m)^{2}$ ..........(2)
From $(1)$ and $(2)$ , we have $A_{1} = A_{2}$

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Similar questions

Q. In the figure, from one handkerchief from four corners, sectors P, Q, R, S each of 2 cm are cut, whose sum is P + Q + R + S =

A_{1}

and a circle of diameter 4 cm from the centre is cut whose area is

A_{2}

, then .................... is possible

If $a_{1}, a_{2}, a_{3}, a_{4}$ are the magnitude of the coordinates at which the circle cuts the axes as shown in the figure. Then what the sum of x and y intercepts.

Q. Let

a_{1}, a_{2}, a_{3} \dots

be terms of A.P.

I f \frac{a_{1} + a_{2} + \dots a_{p}}{a_{1} + a_{2} + \dots + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q,

then

\frac{a_{6}}{a_{21}}

equal

Q. The chord of the contact of tangents from a point

P

to a circle passes through

Q

(

Q

lies outside the circle). If

a_{1}

and

a_{2}

are the lengths of the tangents from

P

and

Q

to the circle respectively, then

P Q

is equal to

Q. Let

a_{1}, a_{2}, a_{3}, . . . . .

be terms of an

A . P .

\frac{a_{1} + a_{2} + . . . + a_{q}}{a_{1} + a_{2} + . . . + a_{q}} = \frac{p^{2}}{q^{2}}, (p \neq q)

then find

\frac{a_{6}}{a_{21}}

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In the figure, from the handkerchief from four corners, sectors P, Q, R and S each of 2cm are cut, whose sum is P+Q+R+S=A1 and a circle of diameter 4cm from the centre is cut whose area is A2, then ______ is possible.

In the figure, from the handkerchief from four corners, sectors P, Q, R and S each of $2 c m$ are cut, whose sum is $P + Q + R + S = A_{1}$ and a circle of diameter $4 c m$ from the centre is cut whose area is $A_{2}$ , then ______ is possible.