Question

The rectangle of side 8cm and 6cm is inscribed inside the circle find the remaining area of the circle

Answer 1

Answer:

The remaining area of the circle is 30.54 sq. cm.

Step-by-step explanation:

The dimensions of rectangle are 8 cm and 6 cm.

The area of rectangle is

$A=length\times width$

$A_1=8\times 6=48$

The area of rectangle is 48 sq. cm.

The diagonal of rectangle is diameter of circle.

$8^2+6^2=d^2$

$100=d^2$

$10=d$

The diameter of circle is 10. so the radius is 5 cm.

Area of circle is

$A_2=\pi r^2=\pi(5)^2=25 \pi=78.54$

The area of circle is 78.54 sq.cm.

The remaining area of the circle

$A=A_2-A_1=78.54-48=30.54$

Therefore the remaining area of the circle is 30.54 sq. cm.

Answer 2

Answer:  

30.5 cm²

Step-by-step explanation:

Length of the rectangle=8 cm

Breadth of the rectangle=6 cm

Area = length*breadth

Area = 8*6 = 48 cm²

We know, that the diagonal of the rectangle is the diameter of the circle.

That particular diagonal divides the rectangle into 2 congruent right triangles.

So, by Pythagoras Theorem,

8²+6²=diagonal²

⇒36+64 = d²

⇒d=√100

⇒d = 10 cm

Now, the diameter of the circle is 10 cm. So, the radius of the circle = 10/2 = 5 cm.

Area of the circle = πr²

                            = 3.14*5*5

                            = 78.5 cm²

Area of the remaining part of the circle = area of the circle - area of the rectangle.

Area of the remaining part of the circle = 78.5 - 48  

Area of the remaining part of the circle = 30.5 cm².