Final answer:
The correct answer is option B, where the unoccupied volume of the prism is found by calculating the volume of both the prism and the sphere and then subtracting the sphere's volume from the prism's volume, resulting in 3963.2 in³.
Step-by-step explanation:
The correct answer is option B. To find the volume of the prism not occupied by the sphere, we need to calculate the volume of both the rectangular prism and the sphere separately and then subtract the volume of the sphere from the volume of the prism.
The volume of the rectangular prism is calculated using the formula:
Vprism = length × width × height, which in this case is Vprism = 15 in × 18 in × 20 in = 5400 in3.
The volume of the sphere is calculated using the formula:
Vsphere = ⅔× π × r3, where r is the radius of the sphere. For a sphere with a radius of 7 in, Vsphere = ⅔× π × 73 ≈ 1436.8 in3.
Subtracting the sphere's volume from the prism's volume gives us the unoccupied volume: 5400 in3 - 1436.8 in3 = 3963.2 in3. Therefore, option B is the correct answer.