Question

From a square metal sheet of side 28cm ,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.​

Answer 1

$\bf{\Huge{\underline{\boxed{\bf{\red{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}}}$

From a square metal sheet of side 28cm, a circular sheet is cut off.

$\bf{\Large{\underline{\bf{To\:find\::}}}}}}$

The radius of the largest possible circular sheet than can be cut & the area of the remaining sheet.

$\bf{\Huge{\underline{\boxed{\sf{\blue{Explanation\::}}}}}}$

We have,

A square metal sheet of side = 28cm

We know that formula of the square: (side × side)    [sq.units]

→ Area = (28 × 28)cm²

→ Area = 784cm²

Hence, the area of square is 784cm².

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For largest circle to be inscribed to a square:

⇒ Side of square = diameter of circle

$\bf{\boxed{\bf{Diameter=2*r}}}}$

⇒ 28cm = 2 × r

⇒ r = $\bf{\cancel{\frac{28}{2} cm}}$

⇒ r = 14cm.

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• $\bf{\large{\underline{\sf{\pink{Area\:of\:circle\::}}}}}$

$\longmapsto\bf{Area\:of\:circle=\pi r^{2} }$

$\longmapsto\bf{Area\:of\:circle=(\frac{22}{7} *14*14)cm^{2} }$

$\longmapsto\bf{Area\:of\:circle=(\frac{22}{\cancel{7}} *\cancel{14}*14)cm^{2} }$

$\longmapsto\bf{Area\:of\:circle=(22*2*14)cm^{2} }$

$\longmapsto\bf{Area\:of\:circle=616cm^{2} }$

Now,

• $\bf{\Large{\underline{\bf{\purple{The\:area\:of\:remaining\:sheet\::}}}}}$

$\longmapsto\bf{Area\:of\:square\:-\:Area\:of\:circle}$

$\longmapsto\bf{784cm^{2} \:-\:616cm^{2}}$

$\longmapsto\bf{168cm^{2} }$

Thus,

The area of remaining sheet is 168cm².

Answer 2

$\huge{\purple{\boxed{\boxed{\boxed{\purple{\underline{\underline{\green{\mathcal{ANSWER:-}}}}}}}}}}$

Side of square = 28 cm

So the radius of the largest possible circle = 14 cm

Area of remaining sheet = area of square - area of circle

Area of remaining sheet = 28 × 28 - 22/7 × 14 × 14

Area of remaining sheet = 784 - 616

Area of remaining sheet = 168 sq cm

$\huge{\pink{\boxed{\boxed{\boxed{\purple{\underline{\underline{\green{\mathcal{THANKS.}}}}}}}}}}$