Multiple choice

A large solid sphere of diameter 18 cm is melted and recast into several small spheres of diameter 3 cm. The percentage increase in the surface area of the smaller spheres over that of the larger sphere is

  1. 500%

  2. 350%

  3. 450%

  4. 545%
Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

The volume of the large sphere is conserved, so (4/3) pi 9^3 equals N times (4/3) pi 1.5^3, giving N = 216. The original surface area was 4 pi 9^2 = 324 pi, while the new total surface area is 216 * 4 pi 1.5^2 = 1944 pi. The percentage increase is ((1944 pi - 324 pi) / 324 pi) * 100, which equals 500%. The result is 500%.

Keep practicing — related questions