
To name: the dimensions of a cube

Answer to Problem 18HP
The dimension of the cube is
Explanation of Solution
Given:
a surface area is between 10 and 20 square inches
Calculation:
The lateral area L of a square prism is,
Here, P is the perimeter of the base and h is the height the square prism.
The surface area S of a square prism is, S = L + 2B .
Here, L is the lateral area and B is the area of the base.
The base of the prism is a square whose side is l .
The perimeter P of the base of the prism is, P = 4l .
Here, l is the side of the square base.
Substitute P = 4l and h = lin
Thus,
Therefore, the lateral area of the square prism is
Find the surface area of the square prism as follows:
The area B of the base of the prism is,
Here, l is the side of the square base.
Substitute
Therefore, the surface area of the square prism is
The surface area of the cube is between 10 and 20 square inches.
Take the surface area of the cube is 12 square inches.
Thus,
Conclusion:
Therefore, the dimension of the cube is
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