How quickly is the level of the water rising?

Question

a trough in the shape of a triangular prism is being filled at a rate of 5 cc per minute. THe depth and width of the trough are both 50 cm, while the length is 150cm. How quickly is the level of the water rising when it is 30 cm deep?

Answer 1

The volume of a triangular prism = (Triangle area)×Length

Area = width×depth/2

Let y be the depth. Width and depth are equal, so width×depth/2 = y²/2

Volume, V = (150/2)y²

dV/dt = 5 cc/s = 150 y dy/dt

dy/dt = (dV/dt)/(150y)

When y=30 cm

dy/dt = (5)/(150(30)) cm/s