How many kilograms of salt water, (with a density of 1.20 g/cm^3) are needed to fill an aquarium that measures 125.0 ft^3? (Hint: Density can be used as a conversion factor to convert volume to mass.)(Remember to make use of significant figures.)
I haven't the slightest clue as to how to solve this. Any help would be immensely appreciated.
density = mass / volume
so,
mass = density * volume
you just have to convert your units
To solve this problem, you can follow these steps:
Step 1: Convert the volume of the aquarium from ft^3 to cm^3
Given:
Volume of the aquarium = 125.0 ft^3
1 ft = 30.48 cm (exact conversion factor)
1 ft^3 = (30.48 cm)^3 = 28316.8466 cm^3 (rounded to five significant figures)
So, the volume of the aquarium in cm^3 is 125.0 ft^3 x 28316.8466 cm^3/ft^3 = 3,539,605.8 cm^3 (rounded to five significant figures)
Step 2: Find the mass of the salt water using the density conversion factor
Given:
Density of the salt water = 1.20 g/cm^3
Volume of the aquarium = 3,539,605.8 cm^3
Density is defined as mass per unit volume, so we can rearrange the equation to find the mass:
Mass = Density x Volume
Mass = 1.20 g/cm^3 x 3,539,605.8 cm^3 = 4,247,527 g
However, we should convert the mass from grams to kilograms, as requested:
4,247,527 g/ 1000 g/kg = 4247.527 kg (rounded to five significant figures)
Therefore, you would need approximately 4247.527 kilograms of salt water to fill the aquarium.
Please note that in this calculation, we have kept the significant figures consistent throughout the steps.