question_answer 25)

Shazli took a wire of length 44 cm and bent it into the shape of a 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 side? Which figure encloses more area, the circle or the square? \[\left( \text{Take  }\!\!\pi\!\!\text{  = }\frac{\text{22}}{\text{7}} \right)\]

Answer:

                Length of the wire \[=\text{44 cm}\] Let the radius of the circle be r cm. Then, circumference of the circle \[\text{= 2 }\!\!\pi\!\!\text{ r cm}\] According to the question, \[2\pi r=44\] \[\Rightarrow \]               \[2\times \frac{22}{7}\times r=44\] \[\Rightarrow \]               \[\text{r =}\frac{\text{44 }\!\!\times\!\!\text{ 7}}{\text{2 }\!\!\times\!\!\text{ 22}}\text{= 7cm}\] Hence, the radius of that circle is 7 cm. Area of the circle \[=\pi {{r}^{2}}\] \[\text{= }\frac{\text{22}}{\text{7}}{{\text{(7)}}^{\text{2}}}\text{ c}{{\text{m}}^{\text{2}}}\text{ = 154 c}{{\text{m}}^{\text{2}}}\]                 Length of each side of the square \[\text{= }\frac{\text{Perimeter of the square}}{\text{4}}\] \[\text{= }\frac{\text{Length of the wire}}{\text{4}}\text{ = }\frac{\text{44}}{\text{4}}\text{cm = 11cm}\] \[\therefore \] Area of the square \[=\text{side}\times \text{side}\]      \[\text{= 11  }\!\!\times\!\!\text{  11 c}{{\text{m}}^{\text{2}}}\text{= 121 c}{{\text{m}}^{\text{2}}}\] Hence, the circle encloses more area.