Answered

The volume of a fish tank is 30 cubic meters. The length of the tank is 2 m and the width of the tank is 3 m. How tall is the fish tank?

Verified Answer :

  • Identify the volume formula for a rectangular prism: \(V = l \times w \times h\).
  • Substitute the known values: \(30 = 2 \times 3 \times h\).
  • Solve for the unknown height: \(h = 30 / 6\).
  • The calculated height is \(\boxed{5 \text{ m}}\).

Explanation

  1. Analyze the given data and geometric shape

The problem asks for the height of a rectangular fish tank given its volume, length, and width. The data provided is:

  • Volume \(V = 30 \text{ m}^3\)
  • Length \(l = 2 \text{ m}\)
  • Width \(w = 3 \text{ m}\)

We assume the fish tank is a rectangular prism, for which the formula for volume is \(V = l \times w \times h\), where \(h\) represents the height.

  1. Set up the equation and solve for the height

Using the formula for the volume of a rectangular prism:
\[V = l \times w \times h\]
Substitute the known values for volume, length, and width into the equation:
\[30 = 2 \times 3 \times h\]
Next, calculate the product of the length and the width:
\[30 = 6 \times h\]
Now, solve for the height \(h\) by dividing both sides of the equation by 6:
\[h = \frac{30}{6} = 5\]
Thus, the height of the fish tank is 5 meters.

Examples

Understanding how to calculate the dimensions of a volume is essential for many practical tasks. For example, if you are planning to build a custom storage container or a planter box, you can determine how deep (height) it needs to be to hold a specific volume of soil or materials based on the floor space (length and width) you have available. If you have a planter area of 2 meters by 3 meters and you need to hold 30 cubic meters of soil, you now know you must build the sides 5 meters high.