Question

The area of the square that can be inscribed in a circle of 10 cm radius is: - a) 200 cm2 b) 128cm2 c) 64√2cm2 d) 64cm2​

Answer 1

Given :

radius of circle = 10 cm

Thus, Diameter = 2 × radius = 2 × 10 = 20 cm

Now,

In the attachment we get to see that the diameter of circle = diagonal of the square inscribed in the circle

Thus, diagonal of square = 20 cm

We know the formula :

$side \: \: of \: square \: = \frac{d}{ \sqrt{2} }$

Where d = diagonal of the square

So,

putting the value of 'd' in the formula we get :

$\frac{d}{ \sqrt{2} } = \frac{20}{ \sqrt{2} } = \frac{10 \times 2}{ \sqrt{2} } = 10 \sqrt{2}$

Thus side of square = 10√2 cm

Now,

We know :

$area \: \: of \: square = s \times s$

Where S = side of square

Putting the value obtained in the formula we get :

$s \times s = 10 \sqrt{2} \times 10 \sqrt{2} = \ 100 \times 2 =200 {cm}^{2}$

Thus,

Area of Square = 200 cm²

CORRECT OPTION - A) 200 cm²

HOPE THIS HELPS

THANKS

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The area of the square that can be inscribed in a circle of 10 cm radius is

a) 200 cm²

b) 128 cm²

c) 64√2 cm²

d) 64 cm²

EVALUATION

Here the given radius of the circle = 10 cm

Now the the square is inscribed in the circle

So we have

Diagonal of the square = Diameter of the circle

⇒ Diagonal of the square = 2 × 10 cm

⇒ Diagonal of the square = 20 cm

Thus we get

Side of the square

$\displaystyle \sf{ = \frac{20}{ \sqrt{2} } \: \: cm }$

$\displaystyle \sf{ = \frac{20 \sqrt{2} }{ 2 } \: \: cm }$

$\displaystyle \sf{ = 10 \sqrt{2} \: \: cm }$

Hence the required area of the square

$\sf = {(10 \sqrt{2} )}^{2} \: \: {cm}^{2}$

$\sf = 200 \: \: {cm}^{2}$

FINAL ANSWER

Hence the correct option is a) 200 cm²

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