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: 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\(\pi\)
