If the radius of the sphere is increased by 4 cm, its surface area is increased by 464π cm² . What is the volume (in cm³) of the original sphere?
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Correct answer: A
Explanation
The correct answer is option 1 i.e. (15625/6) π
Surface Area = 4πr² (where r is radius of sphere)
Difference = 4π [(r + 4)² - r²] = 464 π
⇒ (r + 4)² - r² = 116
⇒ (2r + 4) (4) = 116
⇒ r = 25/2
Hence,
Volume = (4/3) π (25/2)³ = (15625/6) π cm3