The volume of a box is the amount of space in the box
- The volume of the box using packing cubes is 2340 cubes
- The volume of the box using volume formula is 36.5625 cubic feet
Method 1: Packing cubes
We have:
[tex]L_1 = \frac 14[/tex] ---- the dimension of the cube
The dimension of the box is given as:
[tex]L = 3\frac 34[/tex]
[tex]W = 3[/tex]
[tex]H = 3\frac 14[/tex]
Divide each of these dimensions by the length of the cube.
So, we have:
[tex]n_1 = \frac{L}{L_1} = 3\frac 34 \div \frac 14 = 15[/tex]
[tex]n_2 = \frac{W}{L_1} = 3\div \frac 14 = 12[/tex]
[tex]n_3 = \frac{H}{L_1} = 3\frac 14 \div \frac 14 = 13[/tex]
So, the volume of the box by packing the cubes is:
[tex]V = 15 \times 13 \times 12[/tex]
[tex]V = 2340[/tex]
Method 2: Volume formula
The volume of a box is:
[tex]V = L \times W \times H[/tex]
So, we have:
[tex]V = 3\frac 34 \times 3 \times 3\frac14[/tex]
Convert fractions
[tex]V = \frac{15}{4} \times 3 \times \frac{13}{4}[/tex]
[tex]V = \frac{585}{16}[/tex]
[tex]V = 36.5625ft^3[/tex]
Both methods are correct ways of calculating the volume of the box.
- The method (1) represents the number of cubes the box can contain.
- When this value is multiplied by the volume of 1 cube, the result will be the same as method (2)
Read more about volumes at:
https://brainly.com/question/13338592
