Question

A metal wire bent in the form of a square of largest area encloses an area of 1225 cm². The same wire is now bent to a largest circle.
Find the area of the circle.​

Answer 1

Topic :-

Mensuration

Given :-

A metal wire is bent in the form of a square which encloses an area of 1225 cm². The same wire is now bent into a largest circle.

To Find :-

Area of the circle.

Concept Used :-

Length of wire will be constant.

Solution :-

Area of given square = 1225 cm²

( Side )² = 1225 cm²

Side = 35 cm

So, side of the square is 35 cm.

Length of wire = Perimeter of Wire

Length of wire = 4 × Side

Length of wire = 4 × 35 cm

Length of wire = 140 cm

Now,

Circle is made with this wire, it means length of wire will be equal to perimeter of Circle.

Perimeter of Circle = Length of wire

2πr = 140 cm

2 × (22/7) × r = 140 cm

r = 140 × (7/22) × (1/2)

r = (490/22) cm

r = (245/11) cm

So, the radius of circle is (245/11) cm.

Now,

Area of the circle = πr²

Area of Circle = (22/7) × (245/11)²

Area of Circle = (22/7) × (60025/121)

Area of Circle = 1559.09 cm²

Answer :-

So, area of circle is 1559.09 cm².

Answer 2

given :

Area of the square made wire =1225 cm^2

to find :

the area of the circle

solution-

Area of the square made wire 1225 cm^2

∴ Length (side) = √Area = √1225= 35 cm

Perimeter of wire = 4 × side

= 4 × 35 =140cm

∴ Circumference of circular wire = 140 cm

2πr = 140

2×22/7×r =140cm

r = 140×7/22×1/2

r = 490/22cm

r = 245/11 cm

so, the radius of circle is (245/11)cm.

now, we have the radius of circle so we can easily find the area of circle by using formula

∴ Area of the circle = πr^2

∴ Area of the circle = πr^2

= 22/7 × (245/11)^2

= 22/7 ×60025/121

area of circle = 1559.09cm^2