a student blows a balloon and its volume increa... - JAMB Mathematics 1992 Question
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\(\pi\)
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Correct Option: B
(\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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