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 $\pi$

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 $\pi$

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