A rectangular piece of metal 3 cm high by 6 cm wide has a hole cut in its centre 1 cm high by 4 cm wide as shown in the diagram. As the metal is warmed from 0 °C to 100 °C, what will happen to the dimensions of the hole?
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When a metal object is heated, it expands uniformly in all directions due to thermal expansion. The linear expansion is given by ΔL = αL₀ΔT, where α is the coefficient of linear expansion, L₀ is the original length, and ΔT is the temperature change. This principle applies to any part of the material, including the boundaries of a hole. As the entire metal piece expands outward, the hole also effectively expands. Therefore, both the height and width of the hole will increase.
Final answer: both height and width will increase