Question

Q12.Theareaofthesquarethatcanbeinscribedinacircleofradius8cmis (a)256cm2. (b)128cm2. (c)642cm2. (d)64cm2​

Answer 1

Areas related to circles

Let me write this question once for better understanding.

$\boxed{\begin{array}{l}\bf{\dag \: \: \underline{Question :}} \\ \\ \text{The area of the square that can be} \\ \text{inscribed in a circle of radius 8cm is} \\ \\ \rm{(a) \: 256 \: cm^2} \\ \rm{(b) \: 128 \: cm^2} \\ \rm{(c) \: 642 \: cm^2} \\ \rm{(d) \: 64 \: cm^2}\end{array}}$

According to the given question, we have been given that the radius of a circle is 8cm. With this information, we have been asked to find out the area of square which is inscribed in a circle.

The radius of circle, r = $8 \: cm$

The diameter of circle, d = $2r = 2 \times 8 = 16 \: cm$

Since, square is inscribed in a circle.

Therefore, the diameter of circle = Diagonal of square inscribed in a circle = 16cm.

Now, we know that the area of square if diagonal is given:

$\boxed{\bf{Area_{(square)} = \dfrac{(Diagonal)^2}{2}}}$

By substituting the known value in the formula, we get:

$\implies Area_{(square)} = \dfrac{(16)^2}{2} \\ \\ \implies Area_{(square)} = \cancel{\dfrac{256}{2}} \\ \\ \implies \boxed{\bf{Area_{(square)} = 128}}$

Hence, the area of square is 128cm². So, option (b) is correct.

Answer 2

Answer:

(b) 128 cm

Explanation:

From the figure,

OA = OB = OC = OD = Radius of the circle = 8 cm

Diagonal of the circle = Radius × 2

= 8 × 2

= 16 cm

Let the side of square = a

Then, Diagonal = √2a

Given that:

✓2a = 16

a = 8√2 cm

$\therefore$ Area of the square that can be inscribed in the circle = a²

= (8✓2)²

= 128 cm²