Question

36 am
use the table, along with
dimensional analysis, to convert
the given unit to the unit indicated.
6 kl to dm³

dm³ (round to the nearest hundredth as needed.)
chapter
volume in cubic units capacity
1 cm³ = 1 ml
1 dm³ = 1000 cm³ = 1 l
1 m³ = 1 kl

Explanation:

Step1: Recall unit conversions

From the table, we know that \(1\ m^3 = 1\ kL\) and \(1\ dm^3=1000\ cm^3\) (also, we can relate \(m^3\) and \(dm^3\): since \(1\ m = 10\ dm\), then \(1\ m^3=(10\ dm)^3 = 1000\ dm^3\)). Also, \(1\ kL = 1\ m^3\) and \(1\ m^3=1000\ dm^3\).

Step2: Convert \(kL\) to \(m^3\)

Given \(6\ kL\), and since \(1\ kL = 1\ m^3\), then \(6\ kL=6\ m^3\).

Step3: Convert \(m^3\) to \(dm^3\)

We know that \(1\ m^3 = 1000\ dm^3\). So, to convert \(6\ m^3\) to \(dm^3\), we multiply by \(1000\): \(6\ m^3\times1000\ \frac{dm^3}{m^3}=6000\ dm^3\).

Answer:

\(6000\)