Final answer:
The volumes of cone W and square pyramid X with the same base area and height are the same, as they are both calculated as one third of the product of the base area and height.
Step-by-step explanation:
The question concerns the comparison of the volumes of a cone with radius 8 cm and height 5 cm, and a square pyramid with the same base area and height. To find the volume of each, we use the formulas for volume. For a cone, the formula is Volume of cone = (1/3)πr²h, and for a square pyramid, the formula is Volume of pyramid = (1/3)base area × height. Since they have the same base area and height, the volumes will be directly proportional to these dimensions.
Comparing the given answers:
- Paul: Volume of pyramid X is less than cone W because it has a different shape. (Incorrect, shape does not determine volume in this case).
- Manuel: Volume of pyramid X is greater than cone W because the base areas are equal. (Incorrect, equal base areas do not determine greater volume).
- Paul: Volume of pyramid X is greater than cone W because pyramid X has a smaller height. (Incorrect, both have the same height).
- Manuel: Volume of pyramid X is less than cone W because the shapes are different. (Incorrect, the difference in shape is not a correct explanation for volume difference here).
The correct explanation is that both have the same base area and height, but a pyramid's volume is calculated by the base area multiplied by the height and then divided by 3, just like the cone. Since they have the same base area and height, their volumes will be the same regardless of their shape, given the formulas.