Question

from a square sheet of side 15cm a circle of radius 7 cm is cut out ​

Answer 1

${\boxed{\sf{Appropriate\: question}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎From a square sheet of side 15 cm, a circle of radius 7 cm is cut out. Find the area of remaining sheet.

${\boxed{\sf{Step\:by\:step\: explanation}}}$

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

• Measure of side of square sheet = 15 cm.
• Measure of radius of circle which was cut out = 7 cm.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The area of remaining sheet.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Square]}=Side^2\:sq.units}}}$

$\underline{\boxed{\sf{{Area}_{[Circle]}=\pi r^2\:sq.units}}}$

${\underline{\underline{\bf{Solution:}}}}$

The area of remaining sheet can be found by subtracting the area of part cut out from the total area of the sheet. Here, the total area of sheet equals the area of square and the area of part cut out equals the area of circle. Hence, by subtracting both, we can get the answer.

Area of square sheet:

Inserting the given measure of side in the formula:

$\leadsto{\sf{Side^2\:sq.units}}$

$\:\:\:\:\:\:\:\:\implies{\sf{15^2}}$

$\:\:\:\:\:\:\:\:\implies{\sf{15\times 15}}$

$\:\:\:\:\:\:\:\:\implies\underline{\sf{225\:{cm}^{2}}}$

Area of circular part which was cut out:

By substituting the measure of radius and value of $\sf{\pi}$ in the formula:

$\leadsto{\sf{\pi r^2\:sq.units}}$

The value of $\sf{\pi}$ can be taken as $\sf{\dfrac{22}{7}}$.

$\:\:\:\:\:\:\:\:\implies{\sf{\dfrac{22}{7}\times 7^2}}$

$\:\:\:\:\:\:\:\:\implies{\sf{\dfrac{22}{\cancel{7}}\times \cancel{7}\times 7}}$

$\:\:\:\:\:\:\:\:\implies{\sf{22\times 7}}$

$\:\:\:\:\:\:\:\:\implies\underline{\sf{154\:{cm}^{2}}}$

$\red\bigstar$ Area of remaining sheet:

$\leadsto{\sf{Area\:of\:square-Area\:of\:circle}}$

By inserting the measures,

$\:\:\:\:\:\:\:\:\implies{\sf{225-154}}$

$\:\:\:\:\:\:\:\:\implies{\frak{\red{\underline{\underline{71\:{cm}^{2}}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The area of remaining sheet is 71 cm².

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Answer 2

Correct Question-:

• ‎From a square sheet of side 15 cm, a circle of radius 7 cm is cut out. Find the area of remaining sheet.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Remaining \:Sheet \:=  71cm².}}}}}$

Explanation-:

$\frak{Given \:\: -:} \begin{cases} \sf{The\:side\:of\:Square \:sheet\:is\:= \frak{15cm}} & \\\\ \sf{Radius \:of\:Circle \:of\:=\:\frak{15cm}\:is\:cut\:out\:from\:square\:sheet}\end{cases}$

$\frak{To\:Find \:\: -:} \begin{cases} \sf{The\:area\:of\:Remaining \:sheet\:\:} \end{cases}$

Now

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Square \: =  side× side.}}}}}$

$\frak{Here \:\: -:} \begin{cases} \sf{The\:isde\:of\:Square \:sheet\:\:15cm} \end{cases}$

Now ,

• $\implies{\sf{\large { Area_{Square}= 15 × 15 }}}$
• $\implies{\sf{\large { Area_{Square}= 225cm² }}}$

Then ,

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Square \: =  225cm².}}}}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{  Area\:of\:Circle \:\: =  \pi × ( Radius)².}}}}}$

$\frak{Here \:\: -:} \begin{cases} \sf{The\:Radius \:of\:Circle \:inside\:sheet\:\:7cm} & \\\\ \sf{\pi= \frac{22}{7}}\end{cases}$

• $\implies{\sf{\large { Area_{Circle}= \frac{22}{7} × 7 × 7 }}}$
• $\implies{\sf{\large { Area_{Circle}= 22 × 7 }}}$
• $\implies{\sf{\large { Area_{Circle}= 154cm² }}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Circle \: =  154cm².}}}}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Remaining \:sheet\: =\: Area \:of\:Square \:-\:Area \:of\:Circle .}}}}}$

$\frak{Here \:\: -:} \begin{cases} \sf{The\:area\:of\:Square \:sheet\:is\:= \frak{225cm²}} & \\\\ \sf{Area \:of\:Circle \:of\:=\:\frak{154cm²}\:is\:cut\:out\:from\:square\:sheet}\end{cases}$

• $\implies{\sf{\large { Area_{Remaining\:Sheet}= 225-154 }}}$
• $\implies{\sf{\large { Area_{Remaining\:Sheet}= 71cm² }}}$

Hence,

• $\underline{\boxed{\star{\sf{\blue{  Area \:of\:Remaining \:Sheet \:=  71cm².}}}}}$

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