Final answer:
No, 1000 shoeboxes wouldn't fit in the dimensions of the given 8 ft tall closet.
Step-by-step explanation:
To determine if 1000 shoeboxes can fit in an 8 ft tall closet with a floor that is 5 ft by 8 ft, we need to calculate the volume of each shoebox and then calculate the volume of both the shoeboxes and the closet. The given dimensions of the shoebox are 4/2 inches by 7 inches by 13 1/2 inches. To find the volume, we multiply the three dimensions together: (4/2) x 7 x (13 1/2). Simplifying this expression, we have 2 x 7 x (27/2) = 2 x 7 x 27/2 = 189 cubic inches. Now, let's calculate the volume of the closet. Multiply the dimensions of the closet together: 5 ft x 8 ft x 8 ft = 320 ft³. Finally, divide the volume of the closet by the volume of one shoebox to find out how many shoeboxes can fit in the closet: 320 ft³ / 189 cubic inches = 320 ft³ / (189/12/12/12) ft³ = 320 ft³ / (189/1728) ft³ = 320 ft³ x (1728/189) = 320 ft³ x 9.14 = 2924.8. Rounded down, we can fit 2924 shoeboxes in the closet, which is fewer than 1000, so 1000 shoeboxes would not fit in the given closet.