Answer:
the volume of 8 identical cubes is approximately 386.744 cm³.
Explanation:
Let's assume the side length of a cube is represented by "s."
The total shaded area of two identical cubes is given as 162 cm². Since there are two cubes, each cube contributes half of the total shaded area.
Area of a single cube = (Total shaded area) / 2
= 162 cm² / 2
= 81 cm²
The area of each face of a cube is equal to the side length squared. Therefore, we can set up the equation:
6s² = 81 cm²
Dividing both sides by 6:
s² = 81 cm² / 6
= 13.5 cm²
Taking the square root of both sides:
s = √(13.5 cm²)
≈ 3.674 cm (rounded to three decimal places)
Now that we know the side length of a single cube, we can calculate the volume of 8 identical cubes.
Volume of a single cube = s³
= (3.674 cm)³
≈ 48.343 cm³ (rounded to three decimal places)
Volume of 8 cubes = Volume of a single cube * 8
= 48.343 cm³ * 8
= 386.744 cm³