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Chapter 9: Problem 82

If there are 10 decimeters in a meter, explain why there are not 10 cubic decimeters in a cubic meter.

Short Answer

Expert verified
There are not 10, but rather 1000 cubic decimeters in a cubic meter because the transition from a linear to a cubic measurement involves cubing the linear unit.

Step by step solution

01

Understanding Units

In the metric system, 'deci' is a prefix indicating one-tenth. So, one decimeter is one-tenth of a meter. Therefore, it is correctly understood that there are 10 decimeters in a meter when dealing with linear measurements.
02

Understanding Cubic Measurement

The term 'cubic' refers to an object having three dimensions. When we say 'cubic meter' or 'cubic decimeter', we're talking about volume. For a cube, the volume is calculated by taking the length of one edge and multiplying it by itself twice (length * width * height). Given that all sides are equal in a cube, this is essentially raising the length of one side to the power of three.
03

Relating Decimeters to Meters in Cubic Terms

Since one meter is composed of 10 decimeters, a cubic meter is (10 decimeters) * (10 decimeters) * (10 decimeters), or 10^3 cubic decimeters. Hence, there are 1000 (not 10) cubic decimeters in a cubic meter.

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