A bedroom has a volume of 118 m3 What is its volume in km3?
The correct answer and explanation is:
The volume of the bedroom is given as 118 cubic meters (m³). To convert this volume into cubic kilometers (km³), the correct conversion factor between meters and kilometers must be used.
1 kilometer (km) equals 1,000 meters (m). Therefore, to convert cubic meters to cubic kilometers, the conversion factor must be cubed because volume is a three-dimensional measurement.
The conversion is as follows: 1 km=1,000 m1 \text{ km} = 1,000 \text{ m}
Cubing both sides: 1 km3=(1,000 m)3=1,0003 m3=1,000,000,000 m3=109 m31 \text{ km}^3 = (1,000 \text{ m})^3 = 1,000^3 \text{ m}^3 = 1,000,000,000 \text{ m}^3 = 10^9 \text{ m}^3
This means that: 1 km3=109 m31 \text{ km}^3 = 10^9 \text{ m}^3
To find the volume in km³, divide the volume in m³ by 10910^9: Volume in km3=118 m3109=1.18×10−7 km3\text{Volume in km}^3 = \frac{118 \text{ m}^3}{10^9} = 1.18 \times 10^{-7} \text{ km}^3
Therefore, the volume of the bedroom is: 1.18×10−7 km31.18 \times 10^{-7} \text{ km}^3
Explanation
Volume conversion requires raising the linear conversion factor to the third power because volume involves three dimensions: length, width, and height. One kilometer is 1,000 meters. When converting cubic meters to cubic kilometers, the calculation is based on how many cubic meters fit into one cubic kilometer.
Since one cubic kilometer equals one billion (10^9) cubic meters, any volume measured in cubic meters must be divided by one billion to convert it to cubic kilometers.
In practical terms, cubic kilometers are used to measure extremely large volumes, such as oceans or large geological formations. For a bedroom or any room, cubic meters are much more appropriate because the resulting value in cubic kilometers would be very small and not convenient for everyday use.
By understanding this conversion, it becomes clear why even relatively large volumes in cubic meters translate to extremely small values when converted to cubic kilometers.
The final converted volume, 1.18×10−71.18 \times 10^{-7} km³, indicates the bedroom occupies a tiny fraction of a cubic kilometer, highlighting the vast difference in scale between meters and kilometers when measuring volume.