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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 edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing (a) the volume of the cube and (b) the surface area of the cube.

(a)

To determine

To estimate: The maximum possible error, relative error and percentage error when computing the volume of the cube.

Explanation

Given:

The edge of the cube is 30 cm and possible error in measurement is 0.1 cm.

Calculation:

Let x be the length of the side of the cube.

The volume of the cube is V=x3.

Consider the function f(x)=x3

The differential is dV=f(x)dx (1)

Derivative of the function f(x)=x3 is f(x)=3x2.

Substitute f(x)=3x2 in equation (1),

dV=3x2dx

Substitute x=30 and dx=0.1,

dV=3(30)2(0.1)=3(900)(0.1)=2700(0.1)=270

Thus, the maximum possible error in computing the volume of the cube is dV=270 c

(b)

To determine

To estimate: The maximum possible error, relative error and percentage error when computing the surface area of the cube.

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