Final answer:
The area of the warehouse floor is 2080 square yards, and with half the height filled with boxes, the volume is 7280 cubic yards. A room with a 351 square-foot floor holds 2808 cubic feet of air. The grain silo with a base area of 155 square feet and height of 23 feet has a total volume of 3565 cubic feet.
Step-by-step explanation:
a. To find the area of the warehouse floor, we multiply the length and the width: Area = Length × Width. Therefore, Area = 65 yards × 32 yards = 2080 square yards. For the volume of the boxes that fill the warehouse to half its height, we use Volume = Area × Height. Since the boxes fill half the height (7 yards / 2), the Volume of boxes = 2080 square yards × (7 yards / 2) = 7280 cubic yards.
b. The area of the rectangular room's floor is also found by multiplying length by width: Area = 27 feet × 13 feet = 351 square feet. The volume of air the room holds, which is its capacity, is found by Volume = Area × Ceiling Height. Therefore, Volume of air = 351 square feet × 8 feet = 2808 cubic feet.
c. To find the volume of the grain silo with a circular base, we use Volume = Base Area × Height. Given that the area of the base is 155 square feet and the height is 23 feet, the Volume = 155 square feet × 23 feet = 3565 cubic feet.