Question

20. The perimeter of a square and circumference of a circle are same and each is equal to
44cm. Which of these figures has greater area and by how much?
Aswer me fast with steps ​

Answer 1

Answer:

perimeter is 44

as we know perimeter is sum of all sides

so length of square is 44/4 is 11

so area of square = 11*11 is 121 sq cm

area of the circle =2*pie*radius =44cm

44/7*r=44

=r=44/44*7

=r=7 cm

area=pie*radius square

22/7*7*7=154 sq cm

154 greater than 121

so circle has a greater area by 31

Answer 2

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar{\pmb{\sf{\red{\underline{Given \: that:}}}}}}$

⋆ The perimeter of a square and circumference of a circle are same.

⋆ The perimeter of a square and circumference of a circle = 44 centimetres.

${\bigstar{\pmb{\sf{\red{\underline{To \: find:}}}}}}$

⋆ Which of these figures that are circle and square has greater area and by how much?

${\bigstar{\pmb{\sf{\red{\underline{Solution:}}}}}}$

⋆ Figure circle has greater area and by 33 centimetres square.

${\bigstar{\pmb{\sf{\red{\underline{Related \: diagrams:}}}}}}$

⋆ Diagram related to square, it's perimeter is 44 centimetres.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large x\ cm}\put(4.4,2){\bf\large x\ cm}\end{picture}$

⋆ Diagram related to circle, it's perimeter is 44 centimetres.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\end{picture}$

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${\bigstar{\pmb{\sf{\red{\underline{Using \: concepts:}}}}}}$

⋆ Formula to find perimeter of square.

⋆ Formula to find perimeter of circle

⋆ Formula to find area of circle

⋆ Formula to find area of square

${\bigstar{\pmb{\sf{\red{\underline{Using \: formulas:}}}}}}$

${\small{\underline{\boxed{\sf{\star \: Perimeter \: of \: square \: = 4 \times side}}}}}$

${\small{\underline{\boxed{\sf{\star \: Perimeter \: of \: circle \: = 2 \pi r}}}}}$

${\small{\underline{\boxed{\sf{\star \: Area \: of \: circle \: = \pi r^{2}}}}}}$

${\small{\underline{\boxed{\sf{\star \: Area \: of \: square \: = side \times side}}}}}$

${\bigstar{\pmb{\sf{\red{\underline{Full \: Solution:}}}}}}$

~ Firstly by using formula to find perimeter of square let us find the side of square.

${\sf{:\implies Perimeter \: = 4 \times side}}$

${\sf{:\implies 44 \: = 4 \times side}}$

${\sf{:\implies \dfrac{44}{4} \: = side}}$

${\sf{:\implies \cancel{\dfrac{44}{4}} \: = side}}$

${\sf{:\implies 11 \: = side}}$

${\sf{:\implies Side \: = 11 \: cm}}$

Henceforth, 11 centimetres is the side of the given square.

~ Now by using the formula to find area of square let us find it's area.

${\sf{:\implies Area \: = side \times side}}$

${\sf{:\implies Area \: = 11 \times 11}}$

${\sf{:\implies Area \: = 121 \: cm^{2}}}$

Henceforth, area of square is 121 centimetres square.

~ Now by using the formula to find perimeter of circle let us find the radius lf the circle.

${\sf{:\implies Perimeter \: = 2 \pi r}}$

${\sf{:\implies 44 \: = 2 \times 3.14 \times r}}$

${\sf{:\implies 44 \: = 6.28 \times r}}$

${\sf{:\implies \dfrac{44}{6.28} \: = r}}$

${\sf{:\implies \cancel{\dfrac{44}{6.28}} \: = r}}$

${\sf{:\implies 7 \: \approx r}}$

${\sf{:\implies Radius \: = 7 \: cm}}$

Henceforth, 7 centimetres is the radius of the circle.

~ Now by using the formula to find out the area of circle, let us find area.

${\sf{:\implies Area \: = \pi r^{2}}}$

${\sf{:\implies Area \: = 3.14 \times 7 \times 7}}$

${\sf{:\implies Area \: = 3.14 \times 49}}$

${\sf{:\implies Area \: = 154 \: cm^{2}}}$

Henceforth, 154 centimetres square is the area of the circle.

~ Now let us find that whose area is greater.

${\sf{:\implies Area \: of \: square \: is \: 121 \: cm^{2}}}$

${\sf{:\implies Area \: of \: circle \: is \: 154 \: cm^{2}}}$

${\sf{:\implies 154 \: is \: greater \: than \: 121}}$

Henceforth, 154 > 121. Henceforth, circle have more area than square.

~ Now let's find their difference.

${\sf{:\implies Area \: of \: square \: is \: 121 \: cm^{2}}}$

${\sf{:\implies Area \: of \: circle \: is \: 154 \: cm^{2}}}$

${\sf{:\implies Difference \: = 154-121}}$

${\sf{:\implies 33 \: cm^{2}}}$

Henceforth, from 33 centimetres sq. circle have larger area than figure square.