Find the circumference of a circle that circumscribes a square of side $ 7 ext{ cm}$. $\left( ext{Use } \p

Question

Find the circumference of a circle that circumscribes a square of side $ 7 	ext{ cm}$. $\left( 	ext{Use } \pi = \frac{22}{7}. ight) $

Examoogle · Accepted Answer

The correct answer is Option B: $22\sqrt{2} 	ext{ cm}$. For a square of side 'a' inscribed in a circle, the diagonal of the square is the diameter of the circle. Diameter = $7\sqrt{2}$. Circumference = $\pi 	imes 7\sqrt{2} = \frac{22}{7} 	imes 7\sqrt{2} = 22\sqrt{2}$.

Step-by-Step Solution & Concepts:
Shortcut Trick: For a square of side 'a' inscribed in a circle, the diagonal of the square is the diameter of the circle. Diameter = $7\sqrt{2}$. Circumference = $\pi 	imes 7\sqrt{2} = \frac{22}{7} 	imes 7\sqrt{2} = 22\sqrt{2}$.

Formula Used: $$d = a\sqrt{2}$$, $$C = \pi d$$

Given: Square of side length a = 7 cm is inscribed in a circle, meaning the circle circumscribes the square.

Steps: Identify the relationship: When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle ($d$).. Calculate the diameter: Given the side of the square $a = 7$ cm, we find the diagonal: $d = 7\sqrt{2}$ cm.. Calculate the circumference: Using the circumference formula $C = \pi d$ and substituting $\pi = \frac{22}{7}$ and $d = 7\sqrt{2}$:

Answer: B is correct because the diameter of the circle is the diagonal of the square ($7\sqrt{2}$ cm), making the circumference $22\sqrt{2}$ cm.

Exam Tip: This concept is frequently used in 'Area of Shaded Regions' problems where you subtract the area of an inscribed square from the area of the circle.

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