A wire, when bent in the form of a square, encloses an area of 484 cm². If the same wire is bent to form a circle, find the area of the circ

Question

A wire, when bent in the form of a square, encloses an area of 484 cm². If the same wire is bent to form a circle, find the area of the circle.
please answer with prosedure properly​

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Jasmine 2 months 2021-12-03T09:07:46+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-12-03T09:09:09+00:00

    Answer:

    The area of the circle is 616 cm²

    Step-by-step explanation:

    Area of square = side × side

    Side² = 484

    ⇒ Side² = \sqrt{484}

    ⇒ Side = 22 cm

    ★ Find the perimeter of square

    The perimeter of square = 4 × side

    ⇒ 4 × 22

    ⇒ 88 cm

    Therefore,

    Length of wire = 88 cm

    Circumference of the circle = 2 π r

    ★Find the radius of the circle

    Let,

    The radius of the circle = r

    So,

    ⇒ 2 π r = 88

    ⇒ 2 × 22 / 7 × r = 88

    ⇒ 44 / 7 × r = 88

    ⇒ 44 r = 88 × 7

    ⇒ 44r = 616

    ⇒ r = 616 / 44

    r = 14

    Now,

    Find the area of circle

    The area of circle = π r²

    ⇒ 22 / 7 × 14 × 14

    ⇒ 22 / 7 × 196

    ⇒ 4312 / 7

    ⇒ 616

    Therefore,

    The area of the circle is 616 cm²

    0
    2021-12-03T09:09:40+00:00

    { \bf{ \underline{ \underline{ \red{Solution}}}}}

    { \bf{Side \: of \: square \:  =  \sqrt{area}}}

     =  \sqrt{484}

     = 22cm

    { \bf{ We \: know \: that }}

    { \bf{Perimeter \: of \: square = 4 \times side}}

     = 4 \times 22

     { \mathtt{ \pink{ \underline{ \underline{88}}}}}

    So, perimeter of the square is 88cm

    __________________________

    ✒Radius of circle =2πr

    ✒2πr= 88

    2 \times  \frac{22}{7}  \times r = 88

    r =  \frac{616}{44}

    { \mathtt{ \pink { \underline{ \underline{14}}}}}

    So radius of the circle is 14

    __________________________

    Now

    ✒Area of circle =

    { \bf{ Area \: of \: circle = π {r}^{2}}}

     \frac{22}{7}  \times  {14}^{2}

    { \mathtt{ \green{ \boxed{616}}}}

    So, Area of circle is 616cm^2

    ____________________________________________________

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