a student blows a balloon and its volume increases at a rate of (pi)(20 – t

^{2})cm^{3}S^{-1}after t seconds. If the initial volume is 0 cm^{3}, 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: Option B

##### Explanation

(frac{dv}{dt}) = (pi)(20 – t^{2})cm^{2}S^{-1}

(int)dv = (pi)(20 – t^{2})dt

V = (pi) (int)(20 – t^{2})dt

V = (pi)(20 (frac{t}{3}) – t^{3}) + 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)