Question

a) A circle is inscribed in a square of area 1024 cm? Find the area of the circle​

Answer 1

Answer:

Area of square with side a is a

2

and area of circle with radius r is πr

2

.

Area of square = 36 sq units.

Hence, side =

36

=6 units.

As circle is inscribed in square, so the diameter of the circle = 6.

If the diameter of the circle is 6 then the radius of the circle is 3 as the radius is half of diameter.

Hence, the area of the circle is π(3)

2

=9π

Answer 2

Answer:

804.5cm²

Step-by-step explanation:

Given,

• area of the square,a = 1024cm²

To find,

• area of the circle = ?

To find the area of circle,we must find the side of square :

We know,

• Area of a square,a = s x s
• Area of a circle,a = πr²
• Side of a square = diameter of the circle
• Radius of the circle = diameter by 2 = d/2 or side/2

Now substitute the values in the formulae :-

1)

• area of square,a = s x s
• a = s x s
• 1024 = s²
• s = √1024
• s = 32cm = (d)

2)

• Radius,r = d/2
• r = d/2
• r = 32/2
• r = 16cm

3)

• area of circle,a = πr²
• a = πr²
• a = 22/7 x 16 x 16
• a = 804.5cm²

Hence area of the circle inscribed in the square is 804.5cm²

Hope it helps