A rectangular room 8cm along by 5cm wide contains 120x120x120m of air. Calculate the height of the room.
With those units, this question makes absolutely no sense.
With 8 cm by 5 cm, it would in a very small doll-house
120x120x120m is a linear unit, not volume
if you meant 120x120x120 m^3, it would be enormous
(visualize a large city block as a cube)
Fix your question.
After that, volume = length x width x height
To calculate the height of the room, you need to use the volume formula:
Volume = length × width × height
Given that the length of the room is 8 cm, the width is 5 cm, and the volume is 120 × 120 × 120 m, we need to convert the volume to cubic centimeters (cm³) before solving for the height.
To convert the volume from cubic meters to cubic centimeters, we need to multiply it by 1,000,000,000 since there are 1,000,000 cm³ in 1 m³.
Volume = 120 × 120 × 120 m³
= 1728000 m³
Now, we can convert the volume to cm³:
Volume = 1728000 × (1,000,000 cm³ / 1 m³)
= 1728000000000000 cm³
Now, using the volume formula, we can solve for the height:
1728000000000000 cm³ = 8 cm × 5 cm × height
Simplifying:
1728000000000000 cm³ = 40 cm² × height
To find the height, divide both sides by 40 cm²:
height = 1728000000000000 cm³ / 40 cm²
= 43200000000000 cm
Therefore, the height of the room is 43200000000000 cm.