Question 5 A planning engineer for a new rice mill must present some estimates to his company regarding the capacity of a silo designed to store rice. Rice is poured from a conveyor belt at the top of the silo into the silo. The silo is a cylinder 30 m high with a radius of 60 m. The conveyor carries rice at a rate of 1500 m³/h and the rice maintains a conical shape inside the silo whose radius is 1.5 times its height. (a) If, at a certain time t, the rice pile is 20 m high, how long will it take for the pile to reach the top of the silo? For this question, you can use the fact that the volume of a cone is given by r²h. (b) How fast is the floor area of the rice pile growing when the height of the pile is 20 m? (c) How much room will be left in the floor area of the silo when the rice pile is 20 m high?
Question 5 A planning engineer for a new rice mill must present some estimates to his company regarding the capacity of a silo designed to store rice. Rice is poured from a conveyor belt at the top of the silo into the silo. The silo is a cylinder 30 m high with a radius of 60 m. The conveyor carries rice at a rate of 1500 m³/h and the rice maintains a conical shape inside the silo whose radius is 1.5 times its height. (a) If, at a certain time t, the rice pile is 20 m high, how long will it take for the pile to reach the top of the silo? For this question, you can use the fact that the volume of a cone is given by r²h. (b) How fast is the floor area of the rice pile growing when the height of the pile is 20 m? (c) How much room will be left in the floor area of the silo when the rice pile is 20 m high?
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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Transcribed Image Text:Question 5
A planning engineer for a new rice mill must present some estimates
to his company regarding the capacity of a silo designed to store rice. Rice is poured from a
conveyor belt at the top of the silo into the silo. The silo is a cylinder 30 m high with a radius of
60 m. The conveyor carries rice at a rate of 1500 m³/h and the rice maintains a conical shape
inside the silo whose radius is 1.5 times its height.
(a) If, at a certain time t, the rice pile is 20 m high, how long will it take for the pile to reach
the top of the silo? For this question, you can use the fact that the volume of a cone is given
by r²h.
(b) How fast is the floor area of the rice pile growing when the height of the pile is 20 m?
(c) How much room will be left in the floor area of the silo when the rice pile is 20 m high?
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