Multiple choice

If the radius of the sphere is increased by 4cm, its surface area is increased by (464\pi) cm². What is the volume (in cm³) of the original sphere?

  1. $\(\frac{15625}{6}\pi\)$
  2. $\(\frac{35937}{8}\pi\)$
  3. $\(\frac{11979}{2}\pi\)$
  4. $\(\frac{15625}{8}\pi\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of sphere = 4πr². When radius increases by 4cm, the difference in surface area is 4π[(r+4)² - r²] = 4π(8r + 16) = 464π. Solving: 8r + 16 = 116, so r = 12.5cm. Original volume = (4/3)π(12.5)³ = (4/3)π(1953.125) = 7812.5/3 π = 15625/6 π. Option A matches this value.

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