Problem 27E

27. A water trough is $10 \mathrm{~m}$ long and a cross-section has the shape of an isosceles trapezoid that is $30 \mathrm{~cm}$ wide at the bottom, $80 \mathrm{~cm}$ wide at the top, and has height $50 \mathrm{~cm}$. If the trough is being filled with water at the rate of $0.2 \mathrm{~m}^{3} / \mathrm{min}$, how fast is the water level rising when the water is $30 \mathrm{~cm}$ deep?

 

Step-by-Step Solution