Answer:
[tex]V' = 900\pi[/tex] [tex]in^{3} /sec[/tex]
Step-by-step explanation:
V = [tex]\frac{1}{3} \pi r^{2}h[/tex]
[tex]V' = \frac{2\pi rh *r'}{3} + \frac{\pi r^{2} *h'}{3}[/tex] (using differentiation product rule)
plug known values in for r, h, r', and h'
[tex]V' = \frac{2\pi (10)(40)(4)}{3} + \frac{\pi (10^{2} )(-5)}{3}[/tex]
[tex]V' = \frac{3200\pi }{3} - \frac{500\pi }{3} \\V' = \frac{2700\pi }{3} \\[/tex]
[tex]V' = 900\pi[/tex] [tex]in^{3} /sec[/tex]
