Math, asked by rns2, 1 year ago

A circular wire of radius 42 cm is bent to form a square. find the ratio of their areas

Answers

Answered by Anonymous
1
Given,
Radius of the circle is r
Therefore, area of the circle =pi*r^2
Also,perimeter of the circle =2pi*r
Perimeter of the circle = perimeter of the square
Side of the square = 2pi*r/4
=pi*r/2
Area of the square =(pi*r/2)^2
=pi^2*r^2/4
Ratio=area of circle /area of square
=(pi*r^2)/(pi^2*r^2/4)
=4/pi

Hence, the ratio is 4/pi...
Sorry, if the answer seems a bit too clumsy.
Answered by BlackVenom05
1
Radius of circle = 42cm

circumference \: of \: circle = 2\pi \: r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{22}{7} \times 42cm \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =264cm

Perimeter of Square = 264 cm
[ as the same wire is bent into sq. ]

side \: of \: sq. = \frac{perimeter}{4} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{264}{4} cm \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 66cm

area \: of \: sq. = side \times side \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (66 \times 66)cm^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4356 {cm}^{2}

area \: of \: circle \: = \pi \: {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 42 \times 42 {cm}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5544 {cm}^{2}

ratio \: of \: their \: areas \: = \frac{4356}{5544} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{11}{14} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:

♦ Ratio of their areas = 11:14
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