Final answer:
The question asks for the remaining volume of a right square pyramid after a cone is removed. The volume of the cone is calculated, and this value is subtracted from the volume of the pyramid to find the remaining volume. However, an incorrect value or misunderstanding of the base side resulted in a negative value, signaling the need for recalculation with correct dimensions.
Step-by-step explanation:
The subject of the question is Mathematics, specifically geometry and volume calculations. The grade level could be considered high school since it involves concepts typically taught at that level.
Volume of a Cone
To determine the remaining volume after removing a cone from a right square pyramid, we first calculate the volume of the cone using the formula:
Vcone = ⅓πr2h
Where r is the cone's radius (half the base side of the square base), and h is the cone's height.
For a cone with a square base side of 14 units, the radius r is 7 units (half of 14). Therefore, the volume of the cone is:
Vcone = ⅓π(7)2(15) = 770π ≈ 2419.76 cubic units
Volume of the Pyramid
The volume of the square pyramid is given by:
Vpyramid = ⅓b2h
Where b is the length of the base side of the square, and h is the height of the pyramid. Since the cone was inscribed in the pyramid, the dimensions of the base and height are the same i.e., 14 units and 15 units respectively. Therefore, the volume of the pyramid is:
Vpyramid = ⅓(14)2(15) = 980 cubic units
Remaining Volume Calculation
The remaining volume after the cone is removed from the pyramid is the volume of the pyramid minus the volume of the cone:
Vremaining =Vpyramid - Vcone = 980 - 2419.76 ≈ -1439.76 cubic units
However, since volume cannot be negative, this would indicate a calculation mistake or misunderstanding of the question. The correct volume of the pyramid should be larger than that of the cone; possibly the side of the base was interpreted incorrectly. Recalculation with correct dimensions is required to provide an accurate remaining volume.