Questions: Quiz #4 (7.1-7.4) Question 19 of 30 This quiz: 30 point(s) poss This question: 1 point(s) How many times larger is a cubic meter than a cubic decimeter? A cubic meter is 1000 times larger than a cubic decimeter. (Type a whole number.)

Solution Steps

To determine how many times larger a cubic meter is than a cubic decimeter, we need to understand the relationship between meters and decimeters. Since 1 meter is equal to 10 decimeters, we can calculate the volume in cubic meters and cubic decimeters. A cubic meter is a cube with sides of 1 meter, and a cubic decimeter is a cube with sides of 1 decimeter. Therefore, the volume of a cubic meter is \(1^3\) cubic meters, and the volume of a cubic decimeter is \(0.1^3\) cubic meters. We then divide the volume of a cubic meter by the volume of a cubic decimeter to find how many times larger it is.

We know that \(1 \, \text{meter} = 10 \, \text{decimeters}\). Therefore, to find the volume of a cubic meter in terms of cubic decimeters, we calculate the volume of a cube with a side length of \(1 \, \text{meter}\) and a cube with a side length of \(1 \, \text{decimeter}\).

The volume of a cubic meter is given by: \[ V_{\text{cubic meter}} = 1^3 = 1 \, \text{m}^3 \] The volume of a cubic decimeter is given by: \[ V_{\text{cubic decimeter}} = (0.1 \, \text{m})^3 = 0.001 \, \text{m}^3 \]

To find how many times larger a cubic meter is than a cubic decimeter, we take the ratio of the two volumes: \[ \text{Ratio} = \frac{V_{\text{cubic meter}}}{V_{\text{cubic decimeter}}} = \frac{1 \, \text{m}^3}{0.001 \, \text{m}^3} = 1000 \]

Final Answer