Final answer:
The edge of 1 cube, given the total volume of 20 similar cubes is 10,240 cm³, is 8 cm.
Step-by-step explanation:
To find the edge of 1 cube when the total volume of 20 similar cubes is given (10,240 cm³), we must first find the volume of a single cube and then calculate the cube root of that volume to determine the length of one edge.
First, divide the total volume by the number of cubes:
- Volume of 1 cube = Total volume of 20 cubes ÷ 20
- Volume of 1 cube = 10,240 cm³ ÷ 20
- Volume of 1 cube = 512 cm³
Next, since the volume of a cube is given by the formula V = s³ (where 'V' is volume and 's' is the side length), we can find the side length by taking the cube root of the volume:
- Side length = ∛(Volume of 1 cube)
- Side length = ∛(512 cm³)
- Side length = 8 cm
The edge length of one cube is 8 cm.