Question

The mass of a substance varies directly as the volume of the substance. If a mass of 30 kg of a substance has a volume of 6 liters, what is the volume of 65 kg of the substance?

Answer 1

The volume of 65 kg of the substance is 13 liters.

Explanation:

If a substance's mass varies directly from its volume, it means that the ratio of mass to volume remains constant. In this case, we can calculate the continuous ratio and then use it to find the volume.

Given:

Mass1 = 30 kg

Volume1 = 6 liters

Let's denote the constant ratio as k.

Mass1 / Volume1 = k

30 kg / 6 liters = k

k = 5 kg/liter

Now, we can find the volume2 for a mass of 65 kg using the constant ratio:

Mass2 = 65 kg

Volume2 = ?

Mass2 / Volume2 = k

65 kg / Volume2 = 5 kg/liter

To find Volume2, we can cross multiply:

65 kg = 5 kg/liter * Volume2

Volume2 = 65 kg / 5 kg/liter

Volume2 = 13 liters