Posted by **rachel** on Sunday, October 16, 2011 at 7:56pm.

the cross section of a 5-ft long trough is an isosceles trapezoid with a 2 foot lower base, a 3-foot upper base, and an altitude of 2 feet. water is running into the trough at a rate of 1 cubic foot per minute. how fast is the water level rising when the water is 1 foot deep?

- calculus -
**Steve**, Monday, October 17, 2011 at 12:35pm
Another trapezoid problem?? Oh well, here goes:

Volume is area of base * length

When the water is h feet deep The trapezoid has lower base = 2, upper base = 2 + h/2 (draw a diagram to see why this is so)

So, the volume is 5 * (2 + 2+h/2)/2 * h

= 5/4 * (h^2 + 8h)

dV = 5/4 * (2h + 8) dh

1 = 5/4 * (2+8) * dh

dh = 1/12.5 ft/min

This makes sense. The base of the trough has area 5x2 = 10 ft^2. If it had straight sides, the height would rise 1/10 ft/min.

The top of the trough has area 15 ft^2. If it had straight sides from the top, the height would rise 1/15 ft/min

## Answer this Question

## Related Questions

- calculus - A trough is 9 feet long and 1 foot high. The vertical cross-section ...
- calculus - A trough is 10 feet long and 1 foot high. The vertical cross-section ...
- Calculus - A trough is 3 feet long and 1 foot high. The vertical cross-section ...
- calculus - 6. A trough is in the shape of a triangular prism. It is 5 feet long ...
- Calculus - A trough is triangular in cross section, an isosceles triangle with ...
- Math - Water is flowing into a trough at a rate of 100 cubic centimeters per ...
- calculus - A trough is 12 feet long and 3 feet across at the top. It ends are ...
- calculus/physics - A trough is 2 feet long and 1 foot high. The vertical cross-...
- math - A water trough is 4 m long and its cross-section is an isosceles ...
- math - The trough is in the shape of a triangular prism. It is 5 ft long and its...

More Related Questions