In a rectangular steel plate 2mm thick, 100 round holes with a diameter of 6mm are drilled.

In a rectangular steel plate 2mm thick, 100 round holes with a diameter of 6mm are drilled. What is the weight of the plate if its dimensions are 10cm x 12cm?

Data: s (steel plate thickness) = 2 mm (2 * 10 ^ -3 m); n (number of holes drilled) = 100; d (hole diameter) = 6 mm (6 * 10 ^ -3 m); the dimensions of the plate are 10 cm x 12 cm (0.1 x 0.12 m).

Constants: ρс (steel density) = 7800 kg / m3.

Steel plate mass: m = m1 – m2 = ρс * V1 – n * ρс * V ^ 2 = ρс * a * b * s – n * ρс * 0.25 * Π * d ^ 2 * s = ρс * s * (a * b – n * 0.25 * Π * d ^ 2).

Calculation: m = 7800 * 2 * 10 ^ -3 * (0.1 * 0.1 ^ 2 – 100 * 0.25 * 3.14 * (6 * 10 ^ -3) 2) ≈ 0.143 kg (143 g ).