1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles trapezoid 30 cm wide at the bottom and 60 cm wide at the top. If the trough leaks water at the rate of 2000 cm/min, how fast in cm/min is the water level decreasing when the water is 20 cm deep?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 14E: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral...
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1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an
isosceles trapezoid 30 cm wide at the bottom and 60 cm wide at the top. If the
trough leaks water at the rate of 2000 cm'/min, how fast in cm/min is the water
level decreasing when the water is 20 cm deep?
2. Water is being poured into a spherical bowl of radius 4 cm at a rate of 2 cm/s. How
fast is the water level rising when it is at 2 cm? Hint: The volume of a
hemispherical bowl of radius R when the height of the water is y is:
V = y
Transcribed Image Text:1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles trapezoid 30 cm wide at the bottom and 60 cm wide at the top. If the trough leaks water at the rate of 2000 cm'/min, how fast in cm/min is the water level decreasing when the water is 20 cm deep? 2. Water is being poured into a spherical bowl of radius 4 cm at a rate of 2 cm/s. How fast is the water level rising when it is at 2 cm? Hint: The volume of a hemispherical bowl of radius R when the height of the water is y is: V = y
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