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The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge of the cube changing when the edges are 8 in. long? (Recall that for a cube, V = x³.) in/sec

The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge of the cube changing when the edges are 8 in. long? (Recall that for a cube, V = x³.) in/sec

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge of the cube changing when the edges are 8 in. long? (Recall that for a cube, V = x³.) in/sec
Transcribed Image Text:The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge of the cube changing when the edges are 8 in. long? (Recall that for a cube, V = x³.) in/sec
Expert Solution
Step 1

Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long.

It is required to find the rate at which the length of each edge of cube changing.

It is known that the volume of the cube is V=x3.

Differentiate V=x3 with respect t as shown below.

dVdt=3x2dxdt

 

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