Question

The circle is made of wire. The area of a circle is 154 sq.cm. That wire is used to form rectangle of breadth 10cm. Find the area of that formed rectangle.
1. 120 sq.cm
2. 130 sq.cm
3. 88 sq.cm
4. 80 sq.cm
5. 110 sq.cm

Answer 1

Correct Answer - Option 1 : 120 sq.cm

Given:

The area of the circle = 154 sq.cm

The breadth of the rectangle = 10 cm 

Formula used:

Perimeter of a rectangle = 2(length + breadth)

Circumference of a circle = 2πr

Area of the circle = πr²  

Calculation:

Area of the circle = πr2  = 154 cm²

⇒ Radius of a circle = √(154/π)= 7cm

⇒ Circumference of a circle = 2πr = 2 × 22/7 × 7 = 44cm

⇒ Perimeter of a rectangle = 2(length + breadth)

⇒ 2(l + 10) = 44 

⇒ Length of a rectangle = 22 - 10 = 12 cm

∴ Area of a rectangle = length × breadth = 12 × 10 ⇒ 120 sq.cm