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 is 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\(\pi\)