Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 4.8, Problem 23P

To determine

To find the new volume of wooden cube.

Expert Solution & Answer

Answer to Problem 23P

The volume of new cube is 343cm3 .

Explanation of Solution

Given information: 0.5 cm was planed off each of the six faces of a wooden cube, its volume decreased by 169 cm cube.

Calculation: The required solution is obtained as,

Let x = side of original cube

Volume of original cube = x3 .

x−1= side of new cube

Volume of new cube = (x−1)3 .

The volume of new cube + 169 = volume of original cube.

(x−1)3+169=x3(x−1)(x−1)2+169=x3(x−1)(x2+2x+1)+169=x3x3−2x2+x−x2+2x−1+169=x3x3−3x2+3x+168=x33x2−3x−168=0x2−x−56=0(x−8)(x+7)x=8,−7

Ignore negative value.

x=8 .

(x−1)3=(8−1)3=(7)3=343 is volume of new cube.

Hence, the volume of new cube is 343cm3 .

Chapter 4.8, Problem 22P

Chapter 4.8, Problem 24P

Chapter 4 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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