James has 6 identical boxes shaped like rectangular pyramids. The total volume of all the boxes together is 1,024.8 cubic inches.If each box has a height of 6 inches,what is the base area of each box ?
For each pyramid, V = 1/3 Bh
So, the volume of all six is
6*(1/3)*Bh = 2Bh
Now just plug in your numbers.
To find the base area of each box, we need to divide the total volume of all the boxes by the height of each box.
Given:
- Total volume of all the boxes = 1,024.8 cubic inches
- Height of each box = 6 inches
To find the base area, we can follow these steps:
Step 1: Find the volume of one box
Since all the boxes are identical, we can find the volume of one box by dividing the total volume by the number of boxes.
Volume of one box = Total volume of all the boxes / Number of boxes
Number of boxes = 6 (as given)
Total volume of all the boxes = 1,024.8 cubic inches (as given)
Volume of one box = 1,024.8 / 6
Step 2: Find the base area of one box
The volume of a rectangular pyramid can be calculated using the formula:
Volume = (1/3) * Base Area * Height
Since the height is given as 6 inches, we can rearrange the formula to solve for the base area:
Base Area = (3 * Volume) / Height
Using the volume of one box and the given height, we can calculate the base area of one box.
Base Area = (3 * Volume of one box) / Height
Now, let's substitute the values and calculate:
Base Area = (3 * (1,024.8 / 6)) / 6
Base Area = 51.24 square inches
Therefore, the base area of each box is 51.24 square inches.