Question

A large spherical balloon is being deflated. When the radius of the balloon decreases from 10 ft to 5 ft, approximately how much volume has it lost? A) 825 ft3 B) 3665 ft3 C) 5726 ft3 D) 7259 ft3

Answer 1

V1 = volume of old sphere
V1 = (4/3)*pi*r^3
V1 = (4/3)*pi*10^3
V1 = (4000/3)pi
V1 = 4188.7902047864 <<--- this is approximate

V2 = volume of newsphere
V2 = (4/3)*pi*r^3
V2 = (4/3)*pi*5^3
V2 = (500/3)pi
V2 = 523.598775598299 <<--- this is approximate

Subtract volumes to find that...
Amount of volume lost = V1 - V2
Amount of volume lost = 4188.7902047864 - 523.598775598299
Amount of volume lost = 3665.1914291881
Amount of volume lost = 3665

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Final Answer: 3665 ft^3 (cubic feet)
So the answer is choice B)

Answer 2

volume of a sphere: V=(4/3)πr³
V1=(4/3)π10³
V2=(4/3)π5³
difference: (4/3)π10³-(4/3)π5³=(4/3)π875=3665
the answer is B.