How many cm^(3) are there in 2.5m^(3) ? How many cm3 are there in 2.5 m3?
The Correct Answer and Explanation is:
To convert from cubic meters (m³) to cubic centimeters (cm³), we use the following conversion factor:1 m=100 cm1\ \text{m} = 100\ \text{cm}1 m=100 cm
Since the units are cubed:1 m3=(100 cm)3=1, 000, 000 cm31\ \text{m}^3 = (100\ \text{cm})^3 = 1,\!000,\!000\ \text{cm}^31 m3=(100 cm)3=1,000,000 cm3
Step-by-step Calculation:
Given:2.5 m32.5\ \text{m}^32.5 m3
Multiply by the conversion factor:2.5 m3×1, 000, 000 cm3/m3=2, 500, 000 cm32.5\ \text{m}^3 \times 1,\!000,\!000\ \text{cm}^3/\text{m}^3 = 2,\!500,\!000\ \text{cm}^32.5 m3×1,000,000 cm3/m3=2,500,000 cm3
Final Answer:
2.5 m3=2, 500, 000 cm32.5\ \text{m}^3 = 2,\!500,\!000\ \text{cm}^32.5 m3=2,500,000 cm3
Explanation:
The metric system is based on powers of 10, making conversions straightforward. The prefix “centi-” in centimeter (cm) means one-hundredth (1/100) of a meter. Therefore, there are 100 centimeters in one meter.
When converting from square or cubic units, the conversion factor must also be squared or cubed, respectively. In this case, because the unit is cubic meters (m³), the linear conversion factor of 100 must be cubed:(100)3=1, 000, 000(100)^3 = 1,\!000,\!000(100)3=1,000,000
This means that one cubic meter is equivalent to 1,000,000 cubic centimeters. To find how many cubic centimeters are in 2.5 cubic meters, multiply 2.5 by 1,000,000. The multiplication gives 2,500,000 cm³.
This conversion is commonly used in science and engineering when dealing with volumes. Large volumes are typically measured in cubic meters, while smaller or more precise volumes may be expressed in cubic centimeters. This concept reinforces the importance of understanding both metric prefixes and the effects of dimensional powers in unit conversions.
