a wire is bent in the shape of a rectangle , whose breadth is 15 cm
and length is 30 cm and if the same wire is bent to a circle ,find which shape encloses more area
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Step-by-step explanation:
Length of the rectangle = 30 cm
Breadth of the rectangle = 15 cm
Perimeter of the rectangle = Perimeter of the circle
Perimeter = 2 × (30 + 15) cm
= 2 × 45 cm
= 90 cm
Let the radius of the circle be r cm.
Perimeter of the circle = 2πr
=> 90 = 2 × 22/7 × r
=> 90 = 44/7 × r
=> 90 × 7/44 = r
=> 14.318 cm = r
So, Radius of the circle = 14.318 cm
Area of the rectangle = 30 × 15 cm²
= 450 cm²
Area of the circle = πr²
= 22/7 × (14.318)² cm²
= 22/7 × 14.318 × 14.318 cm²
= 644.3018 cm²
So, from the above calculations, we can see that the circle encloses more area.
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