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From a square metal sheet of side $28 cm$ , a circular sheet is cut off. Find the radius of the largest possible circular sheet that can be cut. Also find the area of the remaining sheet.

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14 cm, 148 c m^{2}

12 cm, 168 c m^{2}

14 cm, 168 c m^{2}

14 cm, 164 c m^{2}

answer is B.

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Detailed Solution

Given, from a square metal sheet of side

28 cm

and a circular sheet is cut off.
Area of square sheet

=

{(28)}^{2} = 784 {cm}^{2}

The largest circle of diameter equal to the side of the square can be cut off from the square sheet.

∴

Radius of circular sheet

=

\frac{28}{2} = 14 cm

Area of remaining sheet

\Rightarrow 784 - π r^{2}

\Rightarrow 784 - \frac{22}{7} \times 14 \times 14

\Rightarrow

784 - 616

\Rightarrow 168

{cm}^{2}

Hence, the required area is 168 sq. cm and radius = 14 cm .
Hence, option 2 is correct.

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