A wood salesperson has a fenced area in which they keep all their wood to keep it organized. The area itself is 12 ft. long and 8 ft. wide. The fence is 8 ft. high. They have bigger pieces of wood that are 4 ft. long and 2 ft. wide and smaller pieces of wood that are 2 ft. long and 1 ft. wide. Each piece of wood is 6 in., or ½ ft., tall.

Answer 1

To calculate the volume of each piece of wood, we first need to convert all dimensions to feet.

For the bigger pieces of wood:
Length: 4 ft
Width: 2 ft
Height: 0.5 ft

Volume = Length x Width x Height
Volume = 4 ft x 2 ft x 0.5 ft
Volume = 4 ft³

For the smaller pieces of wood:
Length: 2 ft
Width: 1 ft
Height: 0.5 ft

Volume = Length x Width x Height
Volume = 2 ft x 1 ft x 0.5 ft
Volume = 1 ft³

Now we need to calculate the total volume of all the wood in the fenced area.

First, we calculate the area of the base of the fenced area:
Area = Length x Width
Area = 12 ft x 8 ft
Area = 96 ft²

Next, we multiply the area by the height of the fence to find the total volume of the fenced area:
Total volume = Area x Height
Total volume = 96 ft² x 8 ft
Total volume = 768 ft³

Now we divide the total volume of the fenced area by the combined volume of the bigger and smaller pieces of wood to find out how many pieces can fit inside:
Total volume / Volume of one big piece = Number of big pieces that can fit
768 ft³ / 4 ft³ = 192 big pieces
Total volume / Volume of one small piece = Number of small pieces that can fit
768 ft³ / 1 ft³ = 768 small pieces

Therefore, the fenced area can hold 192 big pieces of wood and 768 small pieces of wood.