If the radius increases from 3 to 5, how does the circle area change?

• A. 9/25
• B. 25/9
• C. 5/3
• D. 3/5

Answer: (B)

Area grows with the square of the radius. Since A = πr^2, changing the radius from 3 to 5 multiplies the area by (5^2)/(3^2) = 25/9. So the new area is 25/9 times the original area, about 2.78 times larger. The fraction 25/9 is the correct description of the change. Fractions like 9/25 would be the reciprocal, and 5/3 or 3/5 reflect only the linear change in radius, not the area.