
(a)
To find: the surface area of the cube.
(a)

Answer to Problem 15PPS
The surface area of the cube is
Explanation of Solution
Given:
Formula used:
The surface area S of a square pyramid is S = L + 2B
Calculation:
The objective is to find the surface area of the cube.
The lateral area L of a square pyramid is given by the formula
L = Ph
Where P is the perimeter of the base and h is the height the square pyramid.
The surface area S of a square pyramid is given by the formula
S = L + 2B
Where L 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
Find the surface area of the square box
Put side = 5 in the surface area formula to find the surface area of the cube.
Therefore, the surface area of the cube is
Conclusion:
Therefore, the surface area of the cube is
(b)
To complete: the given table.
(b)

Answer to Problem 15PPS
Scale Factor of Dilation | Original | ||
Length of Side | 5 | ||
Surface Area |
Explanation of Solution
Given:
Scale Factor of Dilation | Original | ||
Length of Side | ■ | ■ | ■ |
Surface Area | ■ | ■ | ■ |
Calculation:
Consider the table
Scale Factor of Dilation | Original | ||
Length of Side | 5 | ||
Surface Area |
The objective is to complete the table.
Put side = 10 in the volume formula to find the surface area of the cube.
Therefore, the surface area of the cube is
Put side = 15 in the volume formula to find the surface area of the cube.
Therefore, the surface area of the cube is
Therefore, the complete table is
Scale Factor of Dilation | Original | ||
Length of Side | 5 | ||
Surface Area |
Conclusion:
Therefore, the given table is completed.
(c)
To compare: the original surface area to the surface area after dilation.
(c)

Answer to Problem 15PPS
The new surface area is 4 times the original surface area when the scale factor is 2
The new surface area is 9 times the original surface area when the scale factor is 3
Explanation of Solution
The objective is to compare the original surface area to the surface are after dilation.
When the side of the cube is dilation by a scale factor 2 the new surface area is 4 times the original surface area.
When the side of the cube is dilation by a scale factor 3 the new surface area is 9 times the original surface area.
(d)
To explain:whether the same relationship exists with rectangular prism or not
(d)

Answer to Problem 15PPS
The same relation exist with the surface are of a rectangular prism
Explanation of Solution
Calculation:
The same relation exist with the surface are of a rectangular prism too because a cube is form of rectangle prism whose sides are equal.
The new surface area is the square of the scale factor of the side multiplied to the original surface area.
The original formula for surface area is
When length and width are double the new surface area becomes
Conclusion:
Therefore, the same relation exist with the surface are of a rectangular prism
Chapter 12 Solutions
Pre-Algebra, Student Edition
Additional Math Textbook Solutions
Introductory Statistics
Intro Stats, Books a la Carte Edition (5th Edition)
Elementary Statistics (13th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Calculus: Early Transcendentals (2nd Edition)
Elementary Statistics
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