   Chapter 9.CR, Problem 3CR 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 height of a square box is 2 in. more than three times the length of a side the base. If the lateral area is 480. in 2 , find the dimensions of the box and volume of the box.

To determine

To find:

The dimensions of the box and volume of the box.

Explanation

Formula used:

Lateral area L of any prism whose altitude has measure h and whose base has perimeter p is given by the formula,

L=ph(1)

Volume of Square Box:

V=a2h(2)

Given:

The height of a square box is 2 in. more than three times the length of a side the base. If the lateral area is 480.in2.

Calculation:

The height of a square box is 2 in. more than three times the length of a side the base.

So, h=2+3a(3)

Where a is the length of a side the base as shown in the figure.

The perimeter of the square box given by the formula,

p=4a

Then the lateral area of the square box is L=480.in2.

We substitute the values h=2+3a,p=4aandL=480

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