Question

To avoid mildew and mold, Clay's new oat barn has an open shaft lengthwise through the barn with small holes drilled throughout that allows gases to escape just in case any wet oats get placed inside the barn. Clay is able to use the entire volume of the barn, except for the air vent shaft, to store oats which he uses for planting crops and feeding his livestock. He has decided to fill the barn to capacity to be prepared for the upcoming winter and planting season. Clay called the Farmers CO-OP and ordered how many cubic feet of oats.

Answer 1

Answer:

Therefore, Clay can order 1,776 cubic feet of oats.

Step-by-step explanation:

To determine how many cubic feet of oats the barn can hold, break the barn up into three sections, the rectangular prism that makes up the bottom section of the barn, the triangular prism that makes up the top of the barn, and the rectangular prism that makes up the shaft.

The rectangular prism that makes up the bottom section of the barn is 12 feet wide, 16 feet long, and 8 feet high. Use the formula for the volume of a rectangular prism to find the volume.

Therefore, the volume of the bottom rectangular prism is 1,536 cubic feet.

The triangular prism that makes up the top section of the barn is 12 feet wide, 4 feet high, and 16 feet long. Use the formula for the volume of a triangular prism to find the volume.

Therefore, the volume of the top triangular prism is 384 cubic feet.The rectangular prism that makes up the shaft through the barn 3 feet wide, 3 feet high, and 16 feet long. Use the formula for the volume of a rectangular prism to find the volume.

Therefore, the volume of the shaft is 144 cubic feet.

The total volume available to store oats is the volume of the bottom section plus the volume of the top section minus the volume of the shaft.