Question

The circumference of a circle is twice the perimeter of a rectangle. the area of the circle is 5544 sq. m. what is the area of the rectangle if the breadth of the rectangle is 10m?



single choice (2, -0.66)



 400



 120



 360



 560

Answer 1

circumference of the circle = twice the perimeter of the rectangle
area of circle = 5544 square metre
area of rectangle = ?
breadth = 10m
radius = ?
now let us find the radius:
area of circle equal to
$\pi \: {r}^{2}$
5544 = 22/7×r square
5544 ×7/22 = r square
1764 = r square
r = root of 1764
r = 42
now let us find length of the rectangle:
circumference = 2 times perimeter (according to the question )
$2 \: \pi \: r \: = 2(2(l + b))$
2 × 22/7 ×42 = 2 × 2× (length+ 10 )
264 = 4× length + 10
264/4 = length + 10
66 - 10 = length
56 = length
now let us find the area of the rectangle:
l × b = 56 × 10
area = 560