If a circle circumscribes a rectangle with side 4 cm and 3 cm, then find the difference between the area of the circle and rectangle?

If a circle circumscribes a rectangle with side 4 cm and 3 cm, then find the difference between the area of the circle and rectangle?
1). 19.625 cm²
2). 12.625 cm²
3). 7.625 cm²
4). 10.625 cm²

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Alin Malya Rashmi G · Answer 1 · 2021-08-24 09:50:31

Solution:

Given : A circle circumscribes a rectangle with,

Length 'l' = 4 cm and Breadth 'b' = 3 cm.

To find : Difference between the area of the circle and rectangle.

Area of rectangle = Length × Breadth

= 4 × 3 = 12 cm²

To find the area of the circle we have to find the diagonal of the rectangle which gives us the diameter of the circle.

To find the diagonal we have to use Pythagoras Theorem.

Diagonal (d) = √( l² + b² )

d = √( 4² + 3² )

d = √( 16 + 9 )

d = √( 25 )

d = 5 cm

We know that,diagonal of rectangle = diameter of circle

Diameter (D) = 5cm

Radius (r) = 5/2 = 2.5 cm

Area of the circle = πr² cm²

Area of the circle = 3.14 × 2.5 × 2.5 cm²

Area of the circle = 19.625 cm²

Difference between the two areas = (19.625 - 12)cm² = 7.625 cm²

So, the correct option is 3). 7.625 cm²

If a circle circumscribes a rectangle with side 4 cm and 3 cm, then find the difference between the area of the circle and rectangle?

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