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a student blows a balloon and its volume increases at a rate of (pi)(20 -…

a student blows a balloon and its volume increases at a rate of (pi)(20 – t2)cm3S-1 after t seconds. If the initial volume is 0 cm3, find the volume of the balloon after 2 seconds
  • A.
    37.00(pi)
  • B.
    37.33(pi)
  • C.
    40.00(pi)
  • D.
    42.67(pi)
Correct Answer: Option B
Explanation

(frac{dv}{dt}) = (pi)(20 – t2)cm2S-1
(int)dv = (pi)(20 – t2)dt
V = (pi) (int)(20 – t2)dt
V = (pi)(20 (frac{t}{3}) – t3) + c
when c = 0, V = (20t – (frac{t^3}{3}))
after t = 2 seconds
V = (pi)(40 – (frac{8}{3})
= (pi)(frac{120 – 8}{3})
= (frac{112}{3})
= 37.33(pi)

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