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A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of 80 inches (in), a width of 60in, and a height of 44in. She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of 8in, widths of 4in, and heights of 2in. How many bricks can the contractor fit in the storage area of her truck?

A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of 8080 inches (in), a width of 60 60 in\mathrm{in} , and a height of 44 44 in\mathrm{in} . She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of 8 8 in\mathrm{in} , widths of 4 4 in\mathrm{in} , and heights of 2 2 in\mathrm{in} . How many bricks can the contractor fit in the storage area of her truck?

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Q. A building contractor has a pickup truck with a rear storage area in the shape of a rectangular prism. The storage area has a length of 8080 inches (in), a width of 60 60 in\mathrm{in} , and a height of 44 44 in\mathrm{in} . She wants to fill the entire storage area with equal-sized rectangular prism-shaped bricks with lengths of 8 8 in\mathrm{in} , widths of 4 4 in\mathrm{in} , and heights of 2 2 in\mathrm{in} . How many bricks can the contractor fit in the storage area of her truck?
  1. Calculate Storage Area Volume: Calculate the volume of the storage area in the pickup truck. The volume of a rectangular prism is given by the formula V=length×width×heightV = \text{length} \times \text{width} \times \text{height}. For the storage area, V=80 in×60 in×44 inV = 80\,\text{in} \times 60\,\text{in} \times 44\,\text{in}. V=80×60×44=211,200V = 80 \times 60 \times 44 = 211,200 cubic inches.
  2. Calculate Brick Volume: Calculate the volume of one brick.\newlineThe volume of a rectangular prism is given by the formula V=length×width×heightV = \text{length} \times \text{width} \times \text{height}. For the brick, V=8 in×4 in×2 inV = 8\,\text{in} \times 4\,\text{in} \times 2\,\text{in}.\newlineV=8×4×2=64V = 8 \times 4 \times 2 = 64 cubic inches.
  3. Determine Number of Bricks: Determine how many bricks can fit in the storage area.\newlineTo find out how many bricks can fit in the storage area, divide the volume of the storage area by the volume of one brick.\newlineNumber of bricks = Volume of storage area / Volume of one brick = 211,200 cubic inches64 cubic inches\frac{211,200 \text{ cubic inches}}{64 \text{ cubic inches}}.\newlineNumber of bricks = 33003300.

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