An empty sandbox has a length of 6 feet width of 4 feet and a depth of 2 feet. If the sandbox is filled with 8 bags of sand and each bag contains 4.5 cubic feet of sand, what fraction of the sandbox is still empty?
V = 6 * 4 * 2
V = 48 cubic feet
8 * 4.5 = 36 cubic feet
36/48 = 3/4 is filled
4/4 - 3/4 = ? empty
To find the fraction of the sandbox that is still empty, we need to first determine the volume of the sandbox and the volume of the sand. Then we can calculate the fraction of the sandbox that is still empty by subtracting the volume of the sand from the volume of the sandbox.
The volume of the sandbox can be found by multiplying its length, width, and depth:
Volume of the sandbox = 6 feet x 4 feet x 2 feet = 48 cubic feet
Next, we need to calculate the volume of the sand. Each bag contains 4.5 cubic feet of sand, and we have 8 bags, so the total volume of the sand is:
Volume of the sand = 4.5 cubic feet/bag x 8 bags = 36 cubic feet
To find the fraction of the sandbox that is still empty, we subtract the volume of the sand from the volume of the sandbox:
Volume of empty space = Volume of the sandbox - Volume of the sand
Volume of empty space = 48 cubic feet - 36 cubic feet = 12 cubic feet
Now, we can calculate the fraction of the sandbox that is still empty by dividing the volume of the empty space by the volume of the sandbox:
Fraction of the sandbox that is empty = Volume of empty space / Volume of the sandbox
Fraction of the sandbox that is empty = 12 cubic feet / 48 cubic feet
Fraction of the sandbox that is empty = 1/4
Therefore, 1/4 or 25% of the sandbox is still empty.