Question

Expanding cube The edges of a cube increase at a rate of $2 \mathrm{cm} / \mathrm{s}$ How fast is the volume changing when the length of each edge is $50 \mathrm{cm} ?$

   Expanding cube The edges of a cube increase at a rate of $2 \mathrm{cm} / \mathrm{s}$ How fast is the volume changing when the length of each edge is $50 \mathrm{cm} ?$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 3, Problem 10

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Solved by Expert Daphne Pusey

06/03/2020

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Step 1: The volume V of a cube is given by the formula $V = s^3$, where s is the length of the side of the cube. Show more…

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Expanding cube The edges of a cube increase at a rate of $2 \mathrm{cm} / \mathrm{s}$ How fast is the volume changing when the length of each edge is $50 \mathrm{cm} ?$

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Key Concepts

Related Rates

Related rates problems involve finding the rate at which one quantity changes by relating it to other quantities that are also changing with time. They require setting up an equation that connects the relevant variables and differentiating with respect to time, allowing us to solve for the desired rate of change.

Chain Rule

The chain rule is a key technique in calculus for differentiating composite functions. In related rates problems, it helps in linking the rate of change of one variable to the rate of change of another variable by accounting for their interdependency with respect to time.

Volume of a Cube

The volume of a cube is calculated using the formula V = s^3, where s represents the length of one edge. Understanding this relationship is crucial in evaluating how the volume changes as the edge length changes, particularly in scenarios where the cube is expanding or contracting.

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