If a match box has inside dimensions of 2 in. by 1 ¼ in. by 5/8 in., find the useful capacity of the box. The cover is made with open ends so that the box can slide into it, the fit being snug. If the match box and cover are made of thin slices of wood 1/22 in. thick, find the amount of wood used in one million boxes
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To find the useful capacity of the box, we first need to calculate the volume of the box. The volume of a rectangular box is given by the formula:
Volume = length * width * height
In this case, the inside dimensions of the matchbox are given as:
Length = 2 inches
Width = 1 ¼ inches = 1.25 inches
Height = 5/8 inches = 0.625 inches
So, the volume of the matchbox is:
Volume = 2 * 1.25 * 0.625 = 1.5625 cubic inches
Now, to find the amount of wood used in constructing the box, we need to consider the thickness of the wood slices used. The given thickness is 1/22 inches.
Since the box has six sides (top, bottom, front, back, left, and right), we need to multiply the volume of the box by the number of sides to consider the thickness of the wood:
Total volume = Volume * number of sides
In this case, the thickness of the wood is 1/22 inches, which means there are 22 slices per inch.
Number of sides = 6 sides
Thickness of the wood = 1/22 inches
Thickness in inches = 1/22
Total volume = 1.5625 * 6 * (1/22) = 0.4242 cubic inches
This means that for one matchbox, 0.4242 cubic inches of wood is used.
To find the amount of wood used in one million boxes, we multiply the amount of wood used in one box by one million:
Amount of wood used = 0.4242 * 1,000,000 = 424,200 cubic inches
Therefore, the amount of wood used in one million matchboxes is 424,200 cubic inches.