   Chapter 9.1, Problem 22E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A cereal box measures 2 in. by 8 in. by 10 in. What is the volume of the box? How many square inches of cardboard make up its surfaces? (Disregard any hidden flaps.)

To determine

To find:

The volume of the cereal box and the number of square inches of cardboard required to make up its surface which measures 2 in. by 8 in. by 10 in.

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.

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

The lateral area (L) of any solid prison with the perimeter of the base of the prism as (P) and altitude ‘h’ is given by the formula

L=Ph.

Here, P is the perimeter of any one of the base of the prism and which is given by the sum of all the sides of the base.

Calculation:

Given,

Dimensions of the box is 2 in., 8 in., by 10 in.

Thus, we have.

l=2 in.

b=8 in.

h=10 in.

Now, the volume of the closed box is given by the formula.

V=lwh

=2 in ·8 in ·10 in

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