Multiple choice

Three circles each of radius $3.5$ cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

  1. $ 3.932\ cm^{ 2 } $
  2. $ 19.251\ cm^{ 2 } $
  3. $ 21.217\ cm^{ 2 } $
  4. $ 1.966\ cm^{ 2 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Three circles of radius r=3.5 form an equilateral triangle of side 2r=7. Area of triangle = (sqrt(3)/4) * side^2 = (1.732/4) * 49 = 21.217. Area of three sectors (each 60 degrees) = 3 * (60/360) * pi * r^2 = 0.5 * 3.14 * 12.25 = 19.2325. Enclosed area = 21.217 - 19.2325 = 1.9845. The closest option is 1.966.