Question

A wire is bent in the form of a circle of radius 42 cm is again bent in the form of a square. What is the sum of numerator and denominator of the ratio in the simplest form of the regions enclosed by the circle and the square?

Answer 1

14/11

Explanation:

a wire is bent in the form of a circle of radius 42cm .

then, length of wire = circumference of circle

= 2πR

where R is the radius of the circle, e.g., R = 42cm

now, length of wire = 2 × 22/7 × 42 = 264 cm

now, again wire is bent in the form of a square .

perimeter of square = length of wire

4 × side length = 264

side length = 66 cm

so, area of square = (66)² cm²

and area of circle = πr² = 22/7 × 42 × 42

= 22 × 6 × 42 cm²

now, ratio of the area enclosed by the circle and the square = (22 × 6 × 42)/66 × 66

= 2 × 42/66 = 14/11