
Concept explainers
(a)
To find: the surface area of the box.
(a)

Answer to Problem 16PPS
The surface area of the box is
Explanation of Solution
Given:
Volume is 576 cubic inches
Length of the box is 12 in.
Width of the box is 8 in..
Formula used:
The surface area S of a rectangular pyramid is S = L + 2B
Calculation:
The objective is to find the surface area of the box.
The volume V of a rectangular box is given by
Wherel is the length, w is the width and h is the height of the rectangular box.
The lateral area L of a rectangular pyramid is given by the formula
L = Ph
WhereP is the perimeter of the base and h is the height the rectangular pyramid.
The surface area S of a rectangular pyramid is given by the formula
S = L + 2B
WhereL is the lateral surface area and B is the area of the base.
On combining the last two formulas, the surface area is given by
First find the height of the rectangular box.
Put V = 576, l = 12 and w = 8 in the volume formula to find height.
Now, find the surface area of the rectangular box.
Put l = 12, w = 8 and h = 6 in the surface area formula to find the surface area.
Conclusion:
Therefore, the surface area of the box is
(b)
To state:which box has greater surface area.
(b)

Answer to Problem 16PPS
The second box has greater surface area than the first box.
Explanation of Solution
Given:
The dimensions of another box 16 in. by 9 in. by 4 in. whose volume is same as that of the first box.
Calculation:
The objective is to state which box has greater surface area.
Find the surface area of the second box.
Put l = 16, w = 9 and h = 4 in the combine formula for surface area to find the surface area of the second box.
Therefore, the surface area of the second box is
Conclusion:
Therefore, the second box has greater surface area than the first box.
(c)
To check: whether the volume of the box is same as the last two boxes and the surface area is greater than the last two boxes
(c)

Answer to Problem 16PPS
The dimensions of the box 16 in. by 18 in. by 2 in. satisfy the condition.
Explanation of Solution
Calculation:
Consider the dimensions of another box 16 in. by 18 in. by 2 in.
The objective is to check whether the volume of the box is same as the last two boxes and the surface area is greater than the last two boxes.
The volume of the box is
Therefore, the volume of the box is
Put l = 16, w = 18 and h = 2 in the combine formula for surface area to find the surface area of the second box.
Therefore, the surface area of the box is
Conclusion:
Therefore, the dimensions of the box 16 in. by 18 in. by 2 in. satisfy the condition.
Chapter 12 Solutions
Pre-Algebra, Student Edition
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