Question

From a square cardboard of side 21 cm, a circle of maximum area is cut out. Find
the area of the cardboard left.
[Hint. Diameter of circle of maximum area = 21 cm.]​

Answer 1

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★ From a square cardboard cardboard of side 21 cm , a circle of maximum area is cut out. Find the area of cardboard left.

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★ Given :

• Side of square = 21 cm

★ To Find :

• The Area of left cardboard = ?

★ Solution :

Since , we have to cut the maximum area ,

So ,

Diameter of the Circle = Side of the square = 21 cm .

• Side(square) = 21 cm
• Radius =
• $\dfrac{21}{2} \sf cm$

So ,

$\rm \mapsto \: area_{left \: cardboard} = total \: area - area_{cut}$

$\mapsto \rm \: area_{ \: left} = area_{square} - area_{circle}$

$\mapsto \rm \: area_{ \: left} = {(side)}^{2} - \pi {r}^{2}$

$\mapsto \rm \: area_{ \: left} = {21}^{2} - \frac{22}{7} \times {( \frac{21}{2}) }^{2} \: {cm}^{2}$

$\mapsto \rm \: area _{left} = 441 - \frac{ \cancel{22}}{ \cancel7} \times \frac{ \cancel{21} \times 21}{ \cancel2 \times 2} \: {cm}^{2}$

$\mapsto \rm \: area_{left} = 441 - 11 \times \frac{3 \times 21}{2} \: {cm}^{2}$

$\mapsto \rm \: area_{left} = 441 - 346.5 \: {cm}^{2}$

$\mapsto\boxed{ \rm \: area_{left} = 94.5 \: {cm}^{2} }$

So ,

The Area of the cardboard left = 94.5 cm²

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★ Formula Used :

• $\sf \: area \: of \: square \: = {side}^{2}$
• $\sf \: area \: of \: circle \: = \pi {r}^{2}$
• $\sf \: radius = \dfrac{diameter}{2}$