Question

if there are 10 decimeters in a meter, explain why there are not 10 cubic decimeters in a cubic meter. choose the correct answer below. a. there are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. this means that there are 10³ cubic decimeters in a cubic meter. b. there are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. this means that there are $\frac{1}{10^{3}}$ cubic decimeters in a cubic meter. c. there are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. this means that there are $\frac{1}{10^{2}}$ cubic decimeters in a cubic meter. d. there are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. this means that there are 10³ cubic decimeters in a cubic meter.

Explanation:

A cubic meter is a unit of volume representing a cube with side - length of 1 meter. Since 1 meter = 10 decimeters, the volume of a 1 - meter cube in decimeters is $(10\text{ dm})\times(10\text{ dm})\times(10\text{ dm})=10^{3}\text{ dm}^3$.

Answer:

D. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means that there are $10^{3}$ cubic decimeters in a cubic meter.