Question

shazil took a wire of length 44 cm and bent it into the shape of circle. find the radius of that circle. also find its area. if the same wire is bent into the shape of a square, what will be the length of each of its sides? which figure encloses more area, the circle or the square?​

Answer 1

Answer:

Step-by-step explanation:

44 cm is the circumference or perimeter

(circumference) 44 cm = 2 π r

                                       =2 × 22 × r

                                              7

                                 r = 44 × 7

                                      22 × 2

                                r = 7

so area = π r²

            =  22×7×7

                     7

             =154

if it is bent into square

    perimeter = 44 cm

    side = 44 ÷ 4

             = 11

and to find which figure encloses more area we should also find the area of the square

so area of square = side × side

                             = 11 × 11

                            = 121

so the circle encloses more area

Answer 2

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❏ Question:-

Shazil took a wire of length 44 cm and bent it into the shape of circle. find the radius of that circle. also find its area. if the same wire is bent into the shape of a square, what will be the length of each of its sides? which figure encloses more area, the circle or the square?

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

❏ Solution:-

✏ Given:-

• length of the wire (l) = 44 cm.

✏ To Find:-

• Radius of the circle (r) = ?
• Area of the Circle (A_{circle}) = ?
• Side of the square (a) = ?
• Area of the square (A_{square}) = ?

✏ Explanation :-

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(3.8,1.2){ 44\:cm }\end{picture}$

Condition:1

Now, This wire is now shaped into a circle ,

$\setlength{\unitlength}{1 cm}\begin{picture}(12,6)\thicklines\put(7.5,7.5){\circle{4}}\put(7.5,7.5){\line(1,0){0.70}}\put(7.7,7.7){ r }\end{picture}$

Let, the radius of the circle is = r cm.

As, the wire is shaped into circle so it's length will be equal to the circumference of that circle,

$\therefore \text{Length of the wire = perimeter of the circle}$

$\sf\implies 44= 2\times\pi\times r$

$\sf\implies 44= 2\times\frac{22}{7}\times</p><p> r$

$\sf\implies r=\frac{\times{44}\times7}{\cancel{22}\times\cancel2}$

$\sf\implies\boxed{\large{\red{r=7\:cm}}}$

Now, area of the circle is

$\sf\implies A_{circle}= \pi r^2$

$\sf\implies A_{circle}= \frac{22}{7} \times7^2\:cm^2$

$\sf\implies A_{circle}= \frac{22}{\cancel7} \times7\times\cancel7\:cm^2$

$\sf\implies A_{circle}= 22 \times7\:cm^2$

$\sf\implies\boxed{\large{\red{A_{circle}=154\:cm^2}}}$

Condition:2

Now, the wire is reshaped into a square,

$\setlength{\unitlength}{1.05 cm}}\begin{picture}(12,4)\thicklines\put(5.6,9.1){ A }\put(5.6,5.8){ B }\put(9.1,5.8){ C }\put(9.05,9.1){ D }\put(4.5,7.5){ a\:cm }\put(7.1,5.3){ a\:cm }\put(9.5,7.5){ a\:cm }\put(7.1,9.5){ a\:cm }\put(6,6){\line(1,0){3}}\put(6,9){\line(1,0){3}}\put(9,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\end{picture}$

Let , the side of the square is = a cm.

As, the wire is shaped into a square shape so it's length will be equal to the perimeter of that square,

$\therefore \text{Length of the wire = perimeter of the square}$

$\sf\implies 44= 4\times side$

$\sf\implies 44= 4\times a$

$\sf\implies a= \frac{\cancel{44}}{\cancel4}$

$\sf\implies\boxed{\large{\red{a=11\:cm}}}$

Now, area of the square is

$\sf\implies A_{square}= a^2$

$\sf\implies A_{square}= 11^2\:cm^2$

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

$\sf\implies\boxed{\large{\red{A_{square}=121\:cm^2}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\end{picture}$

$\bf\therefore\:\:\:\:\large{ A_{\red{circle}} >A_{\red{square}}}$