A wooden log measuring 4 meters in length, 5 decimeters in width, and 3 decimeters in thickness was used to cut 40 planks, each 2 meters long and 2 decimeters wide. 2% of the wood was wasted during cutting, and 108 cubic decimeters of wood still remain in the log. Determine the thickness of each plank.

Q.A wooden log measuring 4 meters in length, 5 decimeters in width, and 3 decimeters in thickness was used to cut 40 planks, each 2 meters long and 2 decimeters wide. 2% of the wood was wasted during cutting, and 108 cubic decimeters of wood still remain in the log. Determine the thickness of each plank.

Length of the wooden log = 4 meters = 40 decimeters Volume of the log = \(40 \times 5 \times 3\) cubic decimeters = 600 cubic decimeters Amount of wood wasted during cutting = \(600 \times \frac{2}{100}\) = 12 cubic decimeters ∴ Total volume of 40 wooden planks = \(600 - (12 + 108)\) = 480 cubic decimeters Length of each plank = 2 meters = 20 decimeters Let the thickness of each plank be \(x\) decimeters ∴ \(20 \times 2 \times x \times 40 = 480\) Or, \(x = \frac{480}{20 \times 2 \times 40}\) Or, \(x = 0.3\) ∴ Each plank was cut with a thickness of 0.3 decimeters.