A rectangular prism with dimensions 6 m × 4 m × 8 m (l×w ×h) is shrinking. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m^3 per minute. Find the height and the volume of the prism at this instant.
A rectangular prism with dimensions 6 m × 4 m × 8 m (l×w ×h) is shrinking. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m^3 per minute. Find the height and the volume of the prism at this instant.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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A rectangular prism with dimensions 6 m × 4 m × 8 m (l×w ×h) is shrinking.
(a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing?
(b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m^3 per minute. Find the height and the volume of the prism at this instant.
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