Multiple choice

Let A and B be two solid spheres, such that the surface area of B is 300% more than that of A. The volume of A is found to be k% lower than that of B. The value of k must be

  1. 85.5

  2. 92.5

  3. 90.5

  4. 87.5

  5. Insufficient data
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area S = 4 * pi * r^2. If S_B = 4 * S_A, then r_B^2 = 4 * r_A^2, so r_B = 2 * r_A. Volume V = (4/3) * pi * r^3. V_B = (4/3) * pi * (2 * r_A)^3 = 8 * V_A. The volume of A is 7/8 of V_B, which is 87.5% lower.

AI explanation

A surface area 300 percent more than sphere A means sphere B has a total surface area 4 times that of A, so its radius is twice that of A. Because the volume of a sphere is proportional to the cube of its radius, sphere B has a volume 8 times that of A, meaning sphere A is 7 over 8 smaller than B. Multiplying this fraction by 100 gives an 87.5 percent decrease, so k equals 87.5.

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