A farmer decides to excavate a rectangular pit in his field, measuring 12 units in length, 6 units in width, and 3 units in depth, to collect rainwater. The soil extracted is then utilized to make 1,000 bricks with dimensions in the ratio 4 : 2 : 1 (length: breadth: height). What is the total surface area of each brick?

The total volume of the rectangular pit is calculated as length times width times depth, giving 12 times 6 times 3, which equals 216 cubic units. Since this volume is used to make 1,000 bricks, the volume of a single brick is 216 divided by 1,000, resulting in 0.216 cubic units. Let the dimensions of the brick be 4x, 2x, and 1x, so the volume is 4x times 2x times 1x, which equals 8x cubed, and setting this equal to 0.216 gives x cubed equals 0.027, meaning x equals 0.3 units. The dimensions of the brick are therefore 1.2 units, 0.6 units, and 0.3 units, and the total surface area is 2 times (1.2 times 0.6 plus 1.2 times 0.3 plus 0.6 times 0.3), which calculates to 2.52 square units.

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