Question

A wire of lenght is 176cm is first bent into a square and then into a circle which one will have more area​

Answer 1

Answer:

Circle

Explanation:

SQUARE:-

Length given = 176cm

perimeter of square = 4 * sides

176 = 4*sides

176/4 = 44cm

Area of square = side * side

                         = 44 * 44

                         = 1936cm2

CIRCLE:-

Length given = 176cm

circumference = 2*Pi*r

176 = 2*Pi*r

176/2 = 88cm

Area of circle = Pi*r2

                       = 88 * 88 * 7/22              [88 * 88* 7 upon 22]

                       = 352 * 7                         [because r2 and our radius is 88]

                       = 2464cm2

therefore area of the circle is greater than area of square.

Answer 2

Given:

Length of the wire = 176 cm

To find:

When the wire is bent into a square and a circle, which one will have more area.

Solution:

$Side of the square = perimeter \div4 = 176 \div 4 =44 \mathrm{~cm} \\\\Area of the square =(\text {Side})^{2}=(44)^{2} \mathrm{~cm}^{2}=1936 cm^{2}\\\\ Circumference of the circle = 2 \pi r =176 \mathrm{~cm}\\\\\begin{aligned}2 \times \frac{22}{7} \times r &=176 \mathrm{~cm} \\r &=\frac{176 \times 7}{2 \times 22}=28 \mathrm{~cm} \\\therefore \text { Area of the circle } &=\pi r^{2} \\&=\frac{22}{7} \times 28 \times 28=2464 \mathrm{~cm}^{2}\end{aligned}$

Area of circle > Area of square.

Therefore, Circle will have a larger area than the square.