Multiple choice

A and B are two metallic solid spheres such that the surface area of B is 800% more than that of A. If the volume of A is x% less than that of B, then the value of x is closest to

  1. 64.2

  2. 72.4

  3. 95.5

  4. 96.3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of a sphere is proportional to r^2. If area of B is 800% more than A, then Area(B) = 9 * Area(A), so r(B) = 3 * r(A). Volume is proportional to r^3, so Volume(B) = 27 * Volume(A). Thus, A is 26/27 of B smaller, which is approximately 96.3%.

AI explanation

A surface area increase of 800% means sphere B has 9 times the surface area of sphere A, making its radius 3 times larger. Since volume is proportional to the cube of the radius, the volume of B is 3³, or 27 times, the volume of A. This means the volume of A is 1/27 of B, making it approximately 96.3% less than the volume of B.

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