What is the capacity of 1000 cm³ in dm³?

Understanding how to convert between different units of volume is a fundamental skill in math and science. Here, we will focus on converting cubic centimeters (cm³) to cubic decimeters (dm³).

Basic Definitions

Cubic Centimeter (cm³)

A cubic centimeter is a unit of volume that represents a cube with each side measuring 1 centimeter. It is commonly used in various scientific and everyday applications to measure small volumes. For instance, the volume of a small bottle of perfume might be measured in cubic centimeters.

Cubic Decimeter (dm³)

A cubic decimeter is a larger unit of volume, representing a cube with each side measuring 1 decimeter. One decimeter is equal to 10 centimeters. Therefore, a cubic decimeter is significantly larger than a cubic centimeter. This unit is often used in contexts where larger volumes are involved, such as the capacity of a car engine or a container of liquid.

Conversion Factor

To convert between cubic centimeters and cubic decimeters, we need to understand the relationship between these units. Since 1 decimeter equals 10 centimeters, we can express this relationship in terms of volume:

$1 text{ dm} = 10 text{ cm}$

When we cube both sides of this equation to convert from linear dimensions to volume, we get:

$(1 text{ dm})^3 = (10 text{ cm})^3$

This simplifies to:

$1 text{ dm}^3 = 1000 text{ cm}^3$

Therefore, 1 cubic decimeter is equal to 1000 cubic centimeters.

Applying the Conversion Factor

Given that we have 1000 cm³ and we want to convert it to dm³, we can use the conversion factor directly:

$1000 text{ cm}^3 times frac{1 text{ dm}^3}{1000 text{ cm}^3} = 1 text{ dm}^3$

So, 1000 cm³ is equivalent to 1 dm³.

Practical Examples

Example 1: Water Bottle

Imagine you have a water bottle with a capacity of 1000 cm³. To find out how many cubic decimeters this is, you use the conversion factor:

$1000 text{ cm}^3 = 1 text{ dm}^3$

So, the water bottle has a capacity of 1 dm³.

Example 2: Aquarium

Suppose you have an aquarium that holds 5000 cm³ of water. To convert this to cubic decimeters, you would divide by 1000:

$frac{5000 text{ cm}^3}{1000} = 5 text{ dm}^3$

Thus, the aquarium holds 5 dm³ of water.

Conclusion

Understanding the conversion between cubic centimeters and cubic decimeters is essential for various practical and scientific applications. By knowing that 1 dm³ is equal to 1000 cm³, you can easily convert between these units of volume. Whether you are measuring the capacity of a bottle, an aquarium, or any other container, this knowledge will help you make accurate and meaningful conversions.

Additional Resources

For further reading and practice, you can refer to these resources:

  2. Wikipedia – Cubic Centimeter
  3. Wikipedia – Cubic Decimeter
  5. National Institute of Standards and Technology – Metric Conversions

1. Wikipedia – Cubic Centimeter2. Wikipedia – Cubic Decimeter

Citations

  1. Khan Academy – Metric Units of Volume
  2. Math is Fun – Volume
  3. 3. Khan Academy – Metric Units of Volume

Related

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H + HO2 → O2 + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O2 k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) H + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-5 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M⁻¹ s⁻¹) 1 OH + H₂ → H + H₂O 3.74 x 10⁷ 2 OH + HO₂ → HO₂ + OH⁻ 5 x 10⁹ 3 OH + H₂O₂ → HO₂ + H₂O 3.8 x 10⁷ 4 OH + O₂ → O₂ + OH 9.96 x 10⁹ 5 OH + HO₂ → O₂ + H₂O 7.1 x 10⁹ 6 OH + OH → H₂O₂ 5.3 x 10⁹ 7 OH + e⁻aq → OH⁻ 3 x 10¹⁰ 8 H + O₂ → HO₂ 2.0 x 10¹⁰ 9 H + HO₂ → H₂O₂ 2.0 x 10¹⁰ 10 H + H₂O₂ → OH + H₂O 3.44 x 10⁷ 11 H + OH → H₂O 1.4 x 10¹⁰ 12 H + H → H₂ 1.94 x 10¹⁰ 13 e⁻aq + O₂ → O₂⁻ 1.9 x 10¹⁰ 14 e⁻aq + O₂ → HO₂⁻ + OH⁻ 1.3 x 10¹⁰ 15 e⁻aq + HO₂ 2.0 x 10¹⁰ 16 e⁻aq + H₂O₂ 1.1 x 10¹⁰ 17 e⁻aq + HO₂ → OH + OH⁻ 1.3 x 10¹⁰ 18 e⁻aq + H⁺ → H 2.3 x 10¹⁰ 19 e⁻aq + e⁻aq → H₂ + OH⁻ + OH⁻ 2.5 x 10⁹ 20 HO₂ + O₂ → O₂ + HO₂ 1.3 x 10⁹ 21 HO₂ + HO₂ → O₂ + H₂O₂ 8.3 x 10⁵ 22 HO₂ + HO₂ → O₂ + OH + H₂O 3.7 23 HO₂ + HO₂ → O₂ + O₂ + OH + H₂O 7 x 10⁵ s⁻¹ 24 H⁺ + O₂⁻ → HO₂ 4.5 x 10¹⁰ 25 H⁺ + O₂⁻ → O₂ 2.0 x 10¹⁰ 26 H⁺ + OH⁻ 1.4 x 10¹¹ 27 H⁺ + HO₂⁻ 2 x 10¹⁰ 28 H₂O₂ → HO₂ + H⁺ + OH⁻ 2.5 x 10⁻⁵ s⁻¹ 29 H₂O₂ → H⁺ + OH⁻ 1.4 x 10⁻⁷ s⁻¹ 30 O₂ + O₂ → O₂ + HO₂ + OH⁻ 0.3 31 O₂ + H₂O₂ → O₂ + OH + OH 16 32

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O + O → 2 OH k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ