Final answer:
To construct the floor frame, approximately 1 piece of 2x10x16' lumber is needed.
Step-by-step explanation:
To determine the total number of 2x10x16' pieces needed to construct the floor frame, we need to find the area of the floor and divide it by the area of each piece. First, let's find the dimensions of the actual floor. Since the scale factor is 1/200, we can multiply the dimensions of the drawing (2x10) by 1/200 to get the actual dimensions in meters (0.01x0.05). The area of the actual floor is then 0.01x0.05 = 0.0005 square meters. Next, we can calculate the area of each piece of lumber. Since each piece is 2x10x16 feet, we convert it to meters by multiplying by 0.3048 (approximately). The area is then 0.6096x0.0381x4.8768 square meters. Finally, we divide the area of the floor by the area of each piece to determine the total number of pieces needed. The calculation is (0.0005 square meters) / (0.6096x0.0381x4.8768 square meters) = approximately 0.002897. Therefore, we would need approximately 0.002897 pieces, which can be rounded up to 1 piece.