To find: the length of the side of the other cube.
Answer to Problem 26HP
The length of the side of the new cube is
Explanation of Solution
Given:
The ratio of the surface areas of two cubes is
The length of one side of the smaller cube is
Calculation:
The objective is to find the length of the side of the other cube.
Let the length of the side of the other cube be
Two solid figures are similar if they have the same shape and their corresponding linear measurements are proportional.
Since both are cubes and their corresponding linear measurements are proportional, so the cubes are similar.
The ratio of the side of smaller cube to larger cube is
The scale factor is
Now, use the property that if two solids are similar with scale factor of
Thus,
where
Therefore, the length of the side of the new cube is approximately
Conclusion:
Therefore, the length of the side of the new cube is approximately
Chapter 12 Solutions
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