A shipping box shaped like a rectangular prism has a height of 6ft and a volume of 96ft3, what is the length and width of the base for the box? Show the description whit a grid.
To find the length and width of the base of the rectangular prism shaped shipping box, we can use the formula for volume of a rectangular prism:
Volume = Length × Width × Height.
Given that the height of the box is 6ft and the volume is 96ft³, we can substitute these values into the formula:
96ft³ = Length × Width × 6ft.
Now, we need to isolate Length and Width to solve for them individually.
Divide both sides of the equation by 6ft:
16ft² = Length × Width.
Since we're looking for two dimensions, we need to find two numbers whose product is 16 and whose sum is the number of square feet (16ft²). We can use a grid to find these numbers:
1 × 16 = 16
2 × 8 = 16
4 × 4 = 16
The pairs of numbers that have a sum equal to the side length (16ft²) are 2 and 8. Therefore, the length and width of the base of the box are 2ft and 8ft, respectively.
Here's a grid representation:
┌───┬───┐
│ H │ H │
├───┼───┤
│ H │ H │
├───┴───┤
│ Length │
├───────┤
│ Width │
├───────┤
│ H │ H │
└───┴───┘
H represents the height (6ft), and the Length and Width represent the base dimensions (2ft and 8ft).
96/6 = 16
All we know is that the base has an area of 16 ft^2. I'm sure you can some up with two factors of 16 which could be the length and width.