Final answer:
The maximum volume of a pyramid that can fit inside an 18 cm cube is calculated by taking one third of the product of the cube's base area and its height, resulting in a volume of 1,944 cm³. Option B is correct.
Step-by-step explanation:
To find the maximum volume of a pyramid that can fit inside a cube where the side of the cube is 18 cm, we should consider a pyramid that has the same base area and height as the cube itself. A cube has six equal sides, and a square-based pyramid that fits exactly inside will have a base that covers the entire bottom face of the cube and a height equal to the side of the cube.
The volume of a pyramid is one third the base area times the height. So, the volume V of the pyramid that fits inside the cube is given by:
V = (1/3) × base area × height
Since the base is a square with side length 18 cm, the base area is 18 cm × 18 cm = 324 cm². The height is the same as the side of the cube, which is 18 cm. So:
V = (1/3) × 324 cm² × 18 cm = 1944 cm³
Therefore, the correct answer is 1,944 cm³ (Option b).
To find the maximum volume of a pyramid that can fit inside a cube, we need to find the cube's volume and divide it by 3. The cube has a side length of 18 cm, so its volume is calculated by cubing the side length: V = 18 cm * 18 cm * 18 cm = 5832 cm³. Finally, dividing the cube's volume by 3 gives us the maximum volume of the pyramid: 5832 cm³ / 3 = 1944 cm³. Therefore, the correct answer is b. 1,944 cm³.