Answer:
The volume of the original clay lamp is 1000 cm³, so the volume of each of the smaller cubes is 1000 cm³ / 4 = 250 cm³.
a) To find the side length of the smaller cubes, we can use the formula for the volume of a cube, which is V = s³, where V is the volume and s is the side length. Rearranging this formula, we get s = V^(1/3).
Substituting V = 250 cm³, we get s = (250 cm³)^(1/3) ≈ 6.30 cm (rounded to two decimal places).
Therefore, the side length of each of the smaller cubes is approximately 6.30 cm.
b) The fourth cube has twice the volume of each of the smaller cubes, so its volume is 2 × 250 cm³ = 500 cm³.
Using the same formula as before, we get s = (500 cm³)^(1/3) ≈ 8.66 cm (rounded to two decimal places).
Therefore, the side length of the larger cube is approximately 8.66 cm