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

JAMB 1992

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 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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