Multiple choice

If the area of a circle is equal to sum of the areas of two circles of diameters $10$ cm and $24$ cm, then the diameter of the larger circle (in cm) is:

  1. $34$
  2. $26$
  3. $17$
  4. $14$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = pi * r^2. Sum of areas = pi * (5^2) + pi * (12^2) = pi * (25 + 144) = 169 * pi. New circle area = pi * R^2 = 169 * pi, so R = 13. Diameter = 2 * R = 26.

AI explanation

The areas of the two smaller circles are found using pi * r^2, yielding pi * 5^2 = 25pi and pi * 12^2 = 144pi. Their combined area is 169pi, which equals the area of the larger circle. Taking the square root of 169 gives the radius of the larger circle as 13 cm, making its diameter 26 cm.

Keep practicing — related questions