The dimensions of the shed are 15m by 3m by 4m. The dimensions of the boxes are 50cm by 40cm by 20cm. What is the maximum number of boxes that can be placed into a storage shed? Show your work.
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Answer:
The dimensions of the shed are 15m by 3m by 4m. The dimensions of the boxes are 50cm by 40cm by 20cm. What is the maximum number of boxes that can be placed into a storage shed? Show your work.
Answer:
Volume is the measure of how much three-dimensional space an object takes up or holds.
Imagine a fish aquarium. Its length, width, and height determine how much water the tank will hold. If you fill it with water, the amount of water is the volume that the tank will hold. You measure volume in cubic units, because you are multiplying three dimensions: length, width, and height.
One way to find the volume of a prism is to consider how many unit cubes it can contain. A unit cube is simply a cube measuring one inch, one centimeter, one foot, or whatever unit of measurement you are using, on all sides. Here are some unit cubes.

To use unit cubes to calculate volume, simply count the number of unit cubes that fit into the prism. Begin by counting the number of cubes that cover the bottom of the prism, and then count each layer. Let’s see how this works.

How many cubes do you see here? If you count all of the cubes, you will see that there are 24 cubes in this prism.
The volume of this prism is 24 units3 or cubic units.
Find the volume of the following figure using unit cubes.

How many cubes are in this figure? If you count the cubes, you will get a total of 48 cubes. The volume of this prism is 48 cubic units or units3.
If you look carefully, you will see that the volume of the rectangular prism is a function of multiplying the length × the width × the height. You just discovered the formula for finding the volume of a rectangular prism. Now let’s refine that formula a little further. Here is the formula.
V=Bh
The volume is equal to the B, base area of the prism, times the height of the prism.
Let's look at an example.
Find the volume of the prism below.

Simply put the values for the length, width, and height in for the appropriate variables in the formula, then solve for V, volume.
First find the area of the base. This is the rectangular side on the bottom. Remember, to find the area of a rectangle, multiply the length times the width.
BBB=lw=16×9=144 cm2
The base area is 144 square centimeters. Now multiply this by the height.
VVV=Bh=144×4=576 cm3
You can use the following formula for volume of a rectangular prism. This combines the two steps that you completed above:
VVV=lwh=(16)(9)(4)=576 cm3
The volume of this rectangular prism is 576 cubic centimeters.
You can work with the same rectangular prism, but fill it with unit cubes.