JAMB - Mathematics (1992 - No. 35)
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
37.00\(\pi\)
37.33\(\pi\)
40.00\(\pi\)
42.67\(\pi\)
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\(\pi\)
\(\int\)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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