Question

the cirrcumference of a circle is equal to the perimeter of a square.if area of the square is 485cm sq,then find rhe area of circle​

Answer 1

circumference of a circle= perimeter of a

square

$2\pi \times r = 4 \times side \: of \: \: square$

pi × r = 4/2 × side

pi × r = 2 × side.......eqn 1

Area of a square= 485

side × side = 485

taking squareroot on both the sides

side = 22.02 cm

substituting side of square 22.02 cm in eqn 1

from eqn 1....

pi × r = 2 × side

pi × r = 2 × 22.02

pi × r = 44.04

r = 44.04/pi

r = 44.04/ pi

now to find area of a circle= pi × r^2

= pi × r × r

= pi × 44.04/ pi × 44.04/ pi

= 44.04 × 44.04 ÷ pi

= 1939.52 / 3.14

= 617.68 sq. cm

Hence the Area of a circle is 617.68 sq. cm