Final answer:
To find the height of the cuboid, we can use the Pythagorean theorem. The height is approximately 8 cm.
Step-by-step explanation:
To find the height of the cuboid, we can use the Pythagorean theorem. The diagonal of the cuboid is the hypotenuse of a right triangle formed by the height, base, and diagonal. Let's label the height as h and the base as b. We can use the equation h^2 + b^2 = diagonal^2 to solve for h. Since the diagonal is 9cm and the base is a square with sides of 4cm, the equation becomes h^2 + 4^2 = 9^2. Simplifying, we get h^2 + 16 = 81. Subtracting 16 from both sides, we have h^2 = 65. Taking the square root of both sides, we find h ≈ 8.06cm. Therefore, the height of the cuboid is approximately 8cm.