Question

14. A rectangular piece of paper is 24 cm, long and 16cm, broad. From its four corners
quadrants of radius 3.5cm each have been cut off. Find the area of the remaining paper.​

Answer 1

$\sf\large\green{\underbrace{Answer\implies 345.5cm^2:-}}}$

$\sf\large\underline\purple{Given:-}$

$\sf{\implies Rectangle\:_{(length)}=24cm}$

$\sf{\implies Rectangle\:_{(breadth)}=16cm}$

$\sf{\implies Quardrants\:_{(radius)}=3.5cm}$

$\sf\large\underline\purple{To\:Find:-}$

$\sf{\implies Area\:_{(remaining\: paper)}=?}$

$\sf\large\underline\purple{Solution:-}$

• To calculate the remaining peice of paper at first we have find the area of rectangular peice of paper and area of quardrants. To find the quardrants we have to apply a formula (1/4 π r²). By applying this we get the area of quardrant then multiply by 4 in its area. After calculating both area of rectangular peice of paper and quardrant we have to subtract to eachother:-]

$\sf\small\underline\orange{Calculation\:for\:rectangle:-}$

$\sf{\implies Rectangle\:_{(area)}=length*breadth}$

$\sf{\implies Rectangle\:_{(area)}=24*16}$

$\sf{\implies Rectangle\:_{(area)}=384cm^2}$

$\sf\small\underline\orange{Calculation\:for\: Quardrant:-}$

$\sf{\implies Quardrant\:_{(area)}=\dfrac{1}{4}\pi\:r^2}$

$\tt{\implies Quardrant\:_{(area)}=\dfrac{1}{4}*\dfrac{22}{7}*3.5^2}$

$\sf{\implies Quardrant\:_{(area)}={22*3.5*3.5}{7*4}}$

$\sf{\implies Quardrant\:_{(area)}=\dfrac{269.5}{28}}$

$\sf{\implies Quardrant\:_{(area)}=9.625cm^2}$

• As you can see above that we get the area a quardrant but in given Question 4 quardrant have been cut so, find area of 4 quardrant=?

$\sf{\implies Area\:_{(4\: quardrant)}=4*Area\:_{(quardrant)}}$

$\sf{\implies Area\:_{(4\: quardrant)}=4*9.625}$

$\sf{\implies Area\:_{(4\: quardrant)}=38.5cm^2}$

• Now calculate the area of remaining peice of paper:-]

$\sf{\implies Area\:_{(remaining\: paper)}=Area\:_{(rectangle)}-Area\:_{(4\: quardrant)}}$

$\sf{\implies Area\:_{(remaining\: paper)}=384-38.5}$

$\sf{\implies Area\:_{(remaining\: paper)}=345.5cm^2}$

$\sf\large{Hence,}$

$\sf\blue{\implies Area\:_{(remaining\: paper)}=345.5cm^2}$

Answer 2

Solution

area of rectangular=length×breadth

=24×16=>384cm²

Area of 4 quadrant=4×1/4 π r²

=>4 × 1/4 × 22/7 ×3.5 × 3.5

=>38.5

so,

Remaining part of paper=384-38.5=345.5 cm²