   Chapter 9.1, Problem 25E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For the box shown, the total area is 94 cm2. Determine the value of x . To determine

To find:

The value of ‘x’ for the box with its total area 94 cm2.

Explanation

The total area of any solid is the area of all the number of lateral sides that it have, including the area of the top and the bottom of solid.

Thus, the total area (T) of any solid prism with its lateral area (L) and base area (B) is given by the formula.

T=L+2B

Here, we have 2B since, any solid prison will have two bases (One upper part and another the lower part).

Calculation:

Given,

Total area of the box =94 cm2

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 cm also

T=94 cm

The total area of the cuboidal box is given by the formula

T =L+2B

=2lh+2wh+2lw

=2lh+wh+2lw

=2lh+wh+lw

T =2(lw+wh+hl)

94=2x+2x+x4+4x+2

94=2x2+2x+4x+4x+8

Combine, the like terms together

94=2x2+10x+8

Divide; by 2 on the both sides,

942=2x2</

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