   Chapter 9.1, Problem 23E 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

The measures of the sides of the square base of a box area twice the measure of the height of the box. If the volume of the box is 108 in3, Find the dimensions of the box.

To determine

To find:

The dimensions of a box such that the measure of the sides of the square base of the box is twice the measure of the height of the box. The volume of the box is 108 in3.

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,

A box with square base and the measure of the side of the box is twice the measure of the height of the box.

Volume of the box =108in3.

Let ‘a’ represent the length and with of the base (side of the square base) of the box and ‘h’ the height of the box.

We have,

Side of the base =2 (Height of the box)

a=2h                                       (1)

Here, the length, width, and height of the box are given by

l=a

b=a

h=h

Also V=108 in3.

The volume of the cuboid box of length ‘l’, width ‘w’, and height ‘h’ is given by

V =lwh

108=a

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