Question

The circumference of a circle is equal to the side of a square whose area measures 407044 cm². What is the area of the circle?
(a) 22583.2 cm²
(b) 32378.5 cm²
(c) 41263.5 cm²
(d) 39483.4 cm²
(e) Cannot be determined

Answer 1

Given,

The circumference of a circle is equal to side of a square whose area is equal to 407044 cm^2

To find,

area of the circle

Main solution:-

Area of a square = Side× Side or S × S

Substituting the values,

S × S = 407044 cm^2

S = √407044 cm^2

= ±638 cm.

Length can't be negative,

So we consider the positive value.

Side = 638 cm

This length of side of this square is equal to the circumference of a circle .

Circumference of a circle = 2πr

Substituting the values,

2πr=638cm

r=638/2π

r = 101.54 cm ( approx )

Area of a circle = πr^2

Substituting the values

Area = π × (101.54)^2

= 32,390.9877 cm^2

We can see that our answer is approximately equal to Option (b).

It is differing because it's not given which value of π we have to take.

Answer : (b)