Question

a circle has been drawn around a rectangle of 6cm and 8cm ,then find the area of the region inside the circle and outside the rectangle​

Answer 1

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.

Answer 2

Answer:

$\huge \underline{ \bf{ \red{Given}}}$

A circle has been drawn around a rectangle of 6cm and 8cm.

Find :- Area of inside the circle and outside the rectangle.

Solution :-

Area of rectangle = length × breadth

= 8×6 = 48 cm ²

The area of rectangle is 48 cm²

From Pythagoras theorm:-

We can find diameter of circle.

${a}^{2} = {8}^{2} + {6}^{2}$

${a}^{2} = 64 + 36$

${a}^{2} = 100$

$a = \sqrt{100}$

$a = 10$

The diameter of circle is 10cm .

In, circle radius is half of diameter

$r = \frac{10}{2}$

$r = 5$

Therefore the radius is 5cm

Area of circle = πr²

$3.14 \times {5}^{2} = 3.14 \times 25 = 78.5cm$

The area of rectangle is 48 cm

The area of circle is 78.5 cm