Question

The area of a circle is equal to the area of a rectangle with sides 112 m and 88 m respectively.Find the circumference of the circle

Answer 1

Answer :

352 m

Step-by-step explanation :

Given that ;

Area of circle = Area of rectangle

Length of rectangle = 112 m

Breadth of rectangle = 88 m

Area of rectangle = ( Length × Breadth ) m²

                               = ( 112 × 88 ) m²

                               = 9856 m²

Now, According to the question ;

Area of circle = 9856 cm²

⇒ π r² = 9856

⇒ 22 / 7 * r² = 9856

⇒ r² = 9856 * 7 / 22

⇒ r² = 3136

⇒ r = √3136

⇒ r = 56 m

Now,

Circumference of circle = 2πr

                                       = 2 * 22 / 7 * 56

                                      = 44 * 8

                                     = 352 m

Hence, the circumference of circle is 352 m.

Answer 2

Question :

The area of a circle is equal to the area of a rectangle with sides 112 m and 88 m respectively. Find the circumference of the circle.

Answer :

The circumference of the circle is 352 m.

Step-by-step explanation :

Given, area of circle = area of rectangle

Length of rectangle, $l=112$ cm

Breadth of rectangle, $b=88$ cm

Since, it is given that area of rectangle is equal to area of circle.

Therefore, area of circle = area of rectangle

⇒ πr² = (112 × 88)

⇒ πr² = 9856

⇒ r² = 9856 / π

⇒ r² = 3136

⇒ r = √3136 = 56

Now, circumference of circle -

⇒ 2πr

⇒ 2 × 22/7 × 56

⇒ 2 × 22 × 8

⇒ 352 m