   Chapter 9.1, Problem 39E 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

Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps? To determine

To find:

The volume of the box formed by folding and sealing the flaps.

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,

Length of the square price of cardboard =24 in.

The measures of the congruent squares that are removed from the four corners =6 in. become the height of the box formed.

Also, the length and width of the base of the box is given by subtracting the lengths of the square piece which are removed from the length of the cardboard.

Thus,

l=24-6+6=24-12=12 in

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