2. Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. Let V is the volume of such a cube with side length x, find (a) Let V is the volume of such a cube with side length x, find a formula for the volume V in terms of x.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 9P: A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can,...
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2.
Sodium chlorate crystals are easy to grow in the shape of cubes by
allowing a solution of water and sodium chlorate to evaporate slowly. Let V is
the volume of such a cube with side length x, find
(a) Let V is the volume of such a cube with side length x, find a formula
for the volume V in terms of x.
(b) Find when x = 4mm.
dV
dr.
(c) Explain the meaning of V′(4) in the context of this problem.
i. V'(4) represents the rate at which the side length is increasing with re-
spect to the volume as x reaches 4 mm. V'(4) represents the volume as
the side length reaches 4 mm.
ii. V'(4) represents the rate at which the volume is increasing with respect
to the side length as x reaches 4 mm.
iii. V'(4) represents the rate at which the volume is increasing with respect
to the side length as V reaches 12 mm³.
iv. V'(4) represents the rate at which the volume is increasing as x reaches
12 mm.
Transcribed Image Text:2. Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. Let V is the volume of such a cube with side length x, find (a) Let V is the volume of such a cube with side length x, find a formula for the volume V in terms of x. (b) Find when x = 4mm. dV dr. (c) Explain the meaning of V′(4) in the context of this problem. i. V'(4) represents the rate at which the side length is increasing with re- spect to the volume as x reaches 4 mm. V'(4) represents the volume as the side length reaches 4 mm. ii. V'(4) represents the rate at which the volume is increasing with respect to the side length as x reaches 4 mm. iii. V'(4) represents the rate at which the volume is increasing with respect to the side length as V reaches 12 mm³. iv. V'(4) represents the rate at which the volume is increasing as x reaches 12 mm.
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