Question

पुस्तकालय अध्यक्ष स्वामी विवेकानंद से मिलकर क्यों हैरान रह गए?​

Answer 1

Answer:

The radius of circle, r = 8 \: cm8cm

The diameter of circle, d = 2r = 2 \times 8 = 16 \: cm2r=2×8=16cm

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}}}

Area

(square)

=

2

(Diagonal)

2

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

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

⟹Area

(square)

=

2

(16)

2

⟹Area

(square)

=

2

256

⟹

Area

(square)

=128

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