Multiple choice

The radii of two circle are $4$ cm and $3$ cm respectively, The diameter of the circle having area equal to the sum of the areas of the two circles(in cm) is

  1. $5$
  2. $7$
  3. $10$
  4. $14$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area = pi * 4^2 + pi * 3^2 = 16pi + 9pi = 25pi. New circle area = pi * R^2 = 25pi, so R = 5. Diameter = 2R = 10.

AI explanation

Using the area of a circle formula, the area of the first circle is π times 4 squared, which is 16π square cm. The area of the second circle is π times 3 squared, which is 9π square cm. Their combined area is 16π plus 9π, totaling 25π square cm. For the new circle, πR^2 equals 25π, so R^2 equals 25 and the radius R is 5 cm; its diameter is twice the radius, giving 10 cm.

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