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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The volume of a cube is increasing at a rate of 10cm3/min. How fast is the surface area increasing when the length of an edge is 30 cm?

To determine

To find: The increasing rate of surface area of the cube when the length of an edge is 30cm.

Explanation

Given:

The volume of cube is increasing at a rate of 10cm3min. That is, dVdt=10.

Let l be the length of an edge of the cube which is 30 cm. That is, l=30.

Calculation:

The volume of cube is, V=l3.

Differentiate on both sides with respect to t.

dVdt=ddt(l3)dVdt=3l31dldtdVdt=3l2dldt

Substitute dVdt=10 and l=30 in the above equation,

10=3(30)2dldt103(900)=dldtdldt=1270

The surface area of cube is A=6l2

Differentiate on both sides with respect to t

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