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The total shaded area of these two identical cubes is 162 cm2. Calculate the volume of 8 such cubes

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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

User Daniil Loban
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