Question

A trough is 10 feet long and its ends have the shape of isosceles triangles that are 3 feet across at the top and 1 foot high. If the trough is filled with water at a rate of 12 feet cubed per minute, how fast is the water level rising when the trough is half a foot deep?

Answer 1

1.6 ft/min

Step-by-step explanation:

Since trough is 10 ft long and water is filled at the rate of 12ft3/min. We can calculate the rate of water filled with respect to area:

= 12 / 10 = 1.2ft2/min

As the water level rises, so does the water surface, or the bottom side of the isosceles triangles. In fact we can calculate the bottom side when the trough is half foot deep:

= 3 / 2 = 1.5 ft

The rate of change in water level would be the same as calculating the height of the isosceles triangles knowing its base

= 1.2 * 2 / 1.5 = 1.6 ft/min