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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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(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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