   Chapter 9.1, Problem 21E 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

Find the volume and the surface area of a closed box that has dimensions of 15 cm, 20 cm, and 0.25 m.(Hint: 1 m = 100 cm.)

To determine

To find:

The volume and the surface area of a “closed box” that has dimensions of 15 cm, 20 cm, and 0.25 m.

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.

The total area of the closed box is given by the sum of the area of the four lateral faces and the area of the two bases.

T=L+2B

Calculation:

Given,

Dimensions of the box is 15 cm, 20 cm, and 0.25 cm.

Thus, we have.

l=15 cm.

b=20 cm.

h=0.25 m.

Of the above three given measures, height of the box is measured by the unit of metre while the other two are measured by the unit of centimeters.

Thus, it is necessary to convert the measure of height from the unit of meter to centimeters, for the units needs to be uniform.

1 meter = 100 centimeter.

Thus,

h= 0

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