The surface area of bag is 800 square inches. The overhead bin to put them in is 102 x 36 x 33 inches. How many of the bags will fit in the overhead bin?
Answer simply and provide evidence.
To find out how many bags will fit in the overhead bin, we need to calculate the volume of the bin and the volume of each bag.
The volume of the overhead bin is given by:
Volume = Length x Width x Height
Volume = 102 inches x 36 inches x 33 inches
Volume = 113,076 cubic inches
Now, let's calculate the volume of each bag. Since we know the surface area of the bag, but not the dimensions, we cannot calculate the volume directly. However, we can determine the volume of a simplified rectangular box that has the same surface area as the bag.
The surface area of a rectangular box is given by:
Surface Area = 2(LW + LH + WH)
Given that the surface area of the bag is 800 square inches, we need to find two numbers that multiply to give 800 and add up to the circumference of the bin (102+36+33=171). The factors of 800 that sum up to 171 are 16 and 50. Therefore, we can assume the dimensions of the simplified rectangular box to be 16 x 50 x 100.
Now we can calculate the volume of the simplified box:
Volume = Length x Width x Height
Volume = 16 inches x 50 inches x 100 inches
Volume = 80,000 cubic inches
To find out how many bags will fit in the overhead bin, we need to divide the volume of the bin by the volume of each bag:
Number of bags = Volume of bin / Volume of each bag
Number of bags = 113,076 cubic inches / 80,000 cubic inches
Number of bags ≈ 1.413
Since we cannot have a fraction of a bag, we conclude that only 1 bag will fit in the overhead bin.
Therefore, only one bag will fit in the overhead bin based on the given dimensions and surface area.