Question

The perimeter of the circle is equal to that of a square. If the area of the circle is π3. Then find out area of the square?
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Answer 1

$\sf \huge\underline{given : }$

• Perimeter of square = Perimeter of Circle.
• Area of circle = π³.

$\sf \huge\underline{ to \: find : }$

• The area of square.

$\sf \huge\underline{ formulae \: used : }$

$\boxed{ \sf{perimeter \: of \: circle =2\pi \: r }} \\ \\ \boxed{ \sf{area \: of \: circle = \pi \: {r}^{2} }} \\ \\ \boxed{ \sf{perimeter \: of \: square = 4 \times side}} \\ \\ \boxed{ \sf{area \: of \: square = {side}^{2} }}$

$\sf \huge\underline{solution : }$

Given that Area(circle) = π³.

Equating with formula,

⇒πr² = π³.

⇒r² = π².

⇒r = π --------(1)

■ Perimeter of circle = 2πr.

From equation (1) ,

Perimeter = 2π.π

Perimeter(circle) = 2π²

Perimeter(circle) = Perimeter(Square)

⇒2π² = 4side

⇒ π² = 2side

⇒side = π²/2 ------(2)

■Area of square = side².

From equation(2),

$\sf{area \: of \: square = { (\frac{ {\pi}^{2} }{2}) }^{2} } \\ \\ \sf{ \therefore \: area \: of \: square = \frac{ {\pi}^{4} }{2} }$

So, area of square = π⁴/2.