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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

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 9 in., 10 in., and 1 ft.

To determine

To find:

The volume and the surface area of a “closed box” that has dimensions of 9 in., 10 in., and 1 ft.

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 9 in., 10 in and 1 ft.

Thus, we have

l= 9 in.

b= 10 in. and

h= 1 ft.

The above three given measures, height of the box is measured by the unit of foot which the other two are measured by the unit of inches.

Thus, it is necessary to convert the measures of height from the unit of foot to inches, for the units need to be uniform.

1 foot =12 inches

Thus,

h=1 ft =12 in

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