Answer:
To determine which liquid storage tank will have the largest capacity, you should calculate the volume of each tank type and compare the results. Let's calculate the volumes for each shape:
1. Cone:
- The volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.
- The height of the cone should be less than or equal to 30 feet, and the base (circle) should fit within the 30-foot cube.
- You would need to calculate the maximum possible volume by varying the radius and height to find the optimal cone shape.
2. Cylinder:
- The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height.
- Similar to the cone, you should calculate the maximum possible volume within the 30-foot cube.
3. Sphere:
- The volume of a sphere is given by V = (4/3)πr³, where r is the radius.
- The sphere's radius should be less than or equal to 15 feet (half the side length of the cube).
4. Square Pyramid:
- The volume of a square pyramid is given by V = (1/3)Bh, where B is the base area and h is the height.
- You would need to calculate the maximum possible volume by varying the base size and height.
Without specific dimensions for each tank, it's challenging to determine which one will have the largest capacity. You should consider the available tank dimensions, ensuring they fit within the 30-foot cube room, and then calculate the volumes for each shape with those specific dimensions. The one with the largest volume will have the highest capacity.