Final answer:
It would take 2 cubes with side lengths of 12 cm to fill the prism.
Step-by-step explanation:
To find the number of cubes with side lengths of 12 cm that are needed to fill the prism, we need to calculate the volume of the prism and divide it by the volume of one cube.
The volume of a prism is given by the formula V = L × W × H, where L is the length, W is the width, and H is the height. Let's assume the length, width, and height of the prism are 20 cm, 15 cm, and 10 cm, respectively.
Therefore, the volume of the prism is V = 20 cm × 15 cm × 10 cm = 3000 cm³.
The volume of one cube with side length 12 cm is V = (12 cm)³ = 1728 cm³.
Now, we can divide the volume of the prism by the volume of one cube to find the number of cubes needed: 3000 cm³ ÷ 1728 cm³ = 1.736 cubic cubes. Since we can't have a fraction of a cube, we would need to round up to the nearest whole number. Therefore, it would take 2 cubes with side lengths of 12 cm to fill the prism.