The density of a fish tank is [tex]$0.3 \frac{\text { fish }}{\text { feet }^3}$[/tex]. There are 15 fish in the tank. What is the volume of the tank?
Answer (2)
The problem provides the density of fish in a tank and the number of fish.
We use the formula for density: D = V N .
Rearrange the formula to solve for volume: V = D N .
Substitute the given values and calculate: V = 0.3 15 = 50 . The volume of the tank is 50 f t 3 .
Explanation
Understanding the Problem We are given the density of a fish tank as 0.3 feet 3 fish and the number of fish in the tank as 15. We need to find the volume of the tank.
Setting up the Equation The density D is defined as the number of fish N per unit volume V , so we have the formula:
D = V N
We are given D = 0.3 and N = 15 . We need to solve for V .
Solving for Volume To find the volume V , we can rearrange the formula:
V = D N
Now, substitute the given values:
V = 0.3 15
Calculating the Result Calculating the volume:
V = 0.3 15 = 50
So, the volume of the fish tank is 50 cubic feet.
Final Answer The volume of the fish tank is 50 cubic feet.
Examples
Understanding density and volume is crucial in many real-world applications. For instance, when designing aquariums or planning storage spaces, knowing the density of the items you're placing helps determine the required volume. In this case, if you knew the density of fish you wanted to keep, you could calculate the necessary tank volume to ensure a healthy environment for the fish. This concept extends to various fields, such as logistics, where calculating the density of packages helps optimize storage and transportation, and even in cooking, where understanding ingredient densities ensures proper recipe scaling.
The volume of the fish tank is calculated using the formula for density, which relates the number of fish to the volume. Given a density of 0.3 fish per cubic foot and 15 fish in total, the volume comes out to be 50 cubic feet. Therefore, the final volume of the tank is 50 cubic feet.
;
