# calculus

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?

1. 👍
2. 👎
3. 👁
1. 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

1. 👍
2. 👎

## Similar Questions

1. ### math

a horizontal trough is 16 meters long and its ends are isosceles trapezoids with an altitude of 4 meters, an upper base of 6 meters and lower base of 4 meters. water is being poured in the trough at a rate of 10 cubic meters per

2. ### Calculus

A trough is 15 ft long and 4 ft across the top, as shown in the figure. Its ends are isosceles triangles with height 3 ft. Water runs into the trough at the rate of 2.5 ft^3/min. How fast is the water level rising when it is 2 ft

3. ### calculus

A water-trough is 10m long and has a cross-section which is the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80cm wide at the top, and has height 50cm. If the trough is being fi lled with water at the rate of

4. ### Calculus

A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is filled with water at a rate of 13 ft3/min, how fast (in ft/min) is the water

1. ### calculus

A trough is 9 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x4 from x=−1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds

2. ### calculus

A trough is 12 feet long and 3 feet across at the top. It ends are isosceles triangles with a height of 3 feet. If water is being pumped into the trough at 2.5 cubic feet per minute, how fast is the water level rising when the

3. ### geometry

An isosceles trapezoid has base angles equal to 45 and bases of lengths 6 and 12. Find the area of the trapezoid.

4. ### calculus

#3 A solid has a base in the form of the ellipse: x^2/25 + y^2/16 = 1. Find the volume if every cross section perpendicular to the x-axis is an isosceles triangle whose altitude is 6 inches. #4 Use the same base and cross sections

1. ### calculus

6. A trough is in the shape of a triangular prism. It is 5 feet long and its vertical cross sections are isosceles triangles with base 2 feet and height 3 feet. Water is being siphoned out of the trough at the rate of 2 cubic feet