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The tower below consists of 4 identical cuboids.
a) With how many percent does the height of the tower change if you remove the orange cuboid from the top?
The initial height is 4a, where "a" is the edge length of each cuboid.
After removing one cuboid, the height is 3a.
The relative change of height is = = = 25%,
and since the height decreases, you can say that the height decreases in 25%, or the change of height is -25%.
b) With how many percent does the height of the tower change if you put the orange cuboid back?
Now the initial height is 3a, while the final height is 4a.
It means that the denominator is 3a in this case.
The change of height is = = = 33.33%.
Solved.
The lesson to learn from this solution is THIS:
Think carefully what is the basic dimension/amount to compare with (or to relate to).
When solving such problems, the denominator always is an INITIAL dimension (amount).
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On percentage, see the lessons
- Percentage problems
- Percentage word problems (Type 1 problems, Finding the Part)
- Percentage word problems (Type 2 problems, Finding the Rate)
- Percentage word problems (Type 3 problems, Finding the Base)
- More complicated percentage problems
- Problems on percentage that lead to unexpected results
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