The area of a circle is \( 49 \pi \mathrm{~cm}^{2} \). Find its radius. (A) \( 7 \pi \mathrm{~cm} \) (B) 7 cm (C) 24.5 cm (D) 49 cm

To find the radius of a circle given its area, you can use the formula for the area of a circle, which is \( A = \pi r^2 \). Here, the area \( A \) is given as \( 49 \pi \, \text{cm}^2 \). Setting that equal to the formula, we have: \[ \pi r^2 = 49 \pi \] Dividing both sides by \( \pi \), we get: \[ r^2 = 49 \] Taking the square root of both sides, we find: \[ r = 7 \, \text{cm} \] So the radius of the circle is \( \textbf{(B) } 7 \, \text{cm} \). --- Did you know that the number \( \pi \) (approximately 3.14) represents the ratio of the circumference of a circle to its diameter? For centuries, mathematicians have celebrated its mysterious properties and endless nature, making it a favorite among number enthusiasts. Many celebrate Pi Day on March 14th (3/14) with pie-eating contests and fun mathematical puzzles! In real life, understanding the geometry of circles is crucial for various fields. Engineers use it for designing circular components in machines, architects rely on circular principles for structures, and even urban planners take advantage of the circle's properties when designing roads. Knowing the radius helps in everything from calculating materials for construction to optimizing layouts in cities!