The building can indeed hold the desired amount of fertilizer since 2134.695 > 576.
Therefore, the building can hold the required fertilizer amount.
Given:
The base width of the cylindrical part is 8 feet.
The total height of the building is 14 feet.
Each dump truck load is 4 feet tall, 6 feet wide, and 12 feet long.
The cylindrical part of the storage building has a height of h1 and the cone-shaped top has a height of h2, where h1 + h2 = 14 feet.
Calculate the volume of the cylindrical part of the storage building.
Volume of a cylinder = π * r^2 * h
where r is the radius and h is the height.
Since the base width is 8 feet, the radius (r) of the cylindrical part is half of that, so r = 4 feet
For the cylindrical part:
Volume_cylinder = π * (4^2) * h1
Next, let's calculate the volume of the cone-shaped top of the storage building.
Volume of a cone = (1/3) * π * r^2 * h
For the cone:
Volume_cone = (1/3) * π * (4^2) * h2
The total volume of the storage building is the sum of the volumes of the cylindrical part and the cone-shaped top:
Total_volume = Volume_cylinder + Volume_cone
We know that the total volume should be able to hold 2 dump-truck loads of fertilizer.
Each dump truck load has a volume of 4 * 6 * 12 = 288 cubic feet.
The amount of fertilizer that can be held by the building is Total_volume / 288.
If h1 = 13 feet, then h2 = 14 - 13 = 1 foot.
plug in the values and calculate:
Volume_cylinder = π * (4^2) * 13 ≈ 2117.94 cubic feet
Volume_cone = (1/3) * π * (4^2) * 1 ≈ 16.755 cubic feet
Total_volume = 2117.94 + 16.755 ≈ 2134.695 cubic feet
check if this volume can hold 2 dump-truck loads of fertilizer:
Total_fertilizer_volume_needed = 2 * 288 ≈ 576 cubic feet
