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 m3 per minute. Find the height and the volume of the prism at this instant.

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 m3 per minute. Find the height and the volume of the prism at this instant.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter12: Quadratic Functions

Section12.6: Solving Problems Involving Quadratic Equations

Problem 1.3E

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Question

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 m3 per minute. Find the height and the volume of the prism at this instant.

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