A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 c

Question

2 years ago

7

A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 70 c

m wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?

Mathematics

1 answer:

ella [17] · Answer 1 · 2022-09-01T13:02:59+03:00

ella [17]2 years ago

7 0

Answer:

dv = surface area * dh

so

dv/dt = surface area * dh/dt

width at surface = 40 + (80-40)(30/40)

= 40 + 30 = 70 cm = 0.70 m

so

surface area = 9 * .7 = 6.3 m^2

so

.3 m^3/min = 6.3 m^2 * dh/dt

and

dh/dt = .047 meters/min or 4.7 cm/min

Step-by-step explanation: