Question

A trough is 10 ft long and it's ends have the shape of isosceles triangles that are 3 ft across at the top and have a height at 1 ft. If the trough is being filled with water at a rate of 12 ft^3/min how fast is the water level rising when the water is 6 inches high?

Answer 1

Hi

Answer 2

from the given information, write an equation for the height of the water level

Answer 3

to find how fast the water level is rising, you would then have to find the derivative and plug in the value

Answer 4

Right

Answer 5

So would equation be V=lwh?

Answer 6

I'm confused

Answer 7

what is l, w , h?

Answer 8

L is 10?

Answer 9

your approach is correct

Answer 10

remember that the area of a triangle is 0.5*b*h

Answer 11

so in this case volume would be...?

Answer 12

Just a second

Answer 13

Well the volume would be the 12

Answer 14

Or dv/dt

Answer 15

why are you thinking about dv/dt?

Answer 16

That's the only thing I know :P I am not good at these

Answer 17

since its a triangular trough, the volume is:
\[v=0.5*b*h*l\]

Answer 18

where b, l and h are given. but since you want to find the water level, you keep h as the variable

Answer 19

Right

Answer 20

I understand why h is left alone cause your finding the rate of the height

Answer 21

wait you need to consider b too since the base changes with height

Answer 22

so your first step would be writing base in terms of height for this specific trough