how to find the length, height and depth of box sides when you know the cubic volume is 216?
Any combintaion of l, h and d for which the product is 216 will work.
There are many ways to build a box.
If the box is cubical, all three dimensions are 6, the cube root of 216.
To find the length, height, and depth of the sides of a box when you know the cubic volume, you can use the formula for the volume of a rectangular prism, which is length × height × depth.
Given that the cubic volume of the box is 216, we know that length × height × depth = 216.
To solve for the dimensions, you can start by finding the prime factorization of 216, which is 2 × 2 × 2 × 3 × 3 × 3.
Since the box dimensions are typically measured in whole numbers, we need to find combinations of these factors that multiply together to give 216.
Here are a few possible combinations that satisfy the equation:
Combination 1:
Length = 6, height = 6, depth = 6
6 × 6 × 6 = 216
Combination 2:
Length = 8, height = 6, depth = 3
8 × 6 × 3 = 216
Combination 3:
Length = 9, height = 4, depth = 6
9 × 4 × 6 = 216
You can continue to find more combinations by arranging the factors differently or using different factors as needed.
Remember that there are multiple solutions to this problem, but these examples should give you a good starting point to find the length, height, and depth of the sides of the box.