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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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If the volume of the box is 252 in3, find the value of x .(See the figure for Exercise 25.)

Chapter 9.1, Problem 26E, If the volume of the box is 252 in3, find the value of x.See the figure for Exercise 25.

To determine

To find:

The value of ‘x’.

Explanation

The volume of any solid is the region of space occupied by it and in general the volume of a solid is given by the product of its base area and altitude.

For a regular solid prism with base area B and altitude h, the volume is given by the formula

V=Bh.

Calculation:

Given,

Volume of the box =252 in3

Also from the given figure, the length ‘l’, width ‘w’, and the height ‘h’ of the box is given by,

l=x+2

w=x

h=4

The volume of the cuboidal box is given by the formula

V=lwh

252=x+2x4

Divide; by 4 on both sides,

2524=x+2x44

63=x+2x

Apply the distributive property of multiplication over addition to the right side

63=x·x+2·x

63=x2+2x

Add; -63 on both sides,

63+-63=x2+2x+-63

0=x2+2x-63

(i

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