A rectangular block has dimensions 150 mm × 80 mm × 60 mm at 25 °C. Its coefficients of linear expansion are $ \alpha_x = 10 \times 10^{-6}\,^{\circ}\!C^{-1} $, $ \alpha_y = 12 \times 10^{-6}\,^{\circ}\!C^{-1} $ and $ \alpha_z = 8 \times 10^{-6}\,^{\circ}\!C^{-1} $ along the respective edges. The block is uniformly heated to 75 °C.

(a) Calculate the new dimensions of the block.

(b) Determine the new volume (in mm³, to the nearest mm³) and the percentage increase in volume (to two decimal places).

Question

A rectangular block has dimensions 150 mm × 80 mm × 60 mm at 25 °C. Its coefficients of linear expansion are $ \alpha_x = 10 \times 10^{-6}\,^{\circ}\!C^{-1} $, $ \alpha_y = 12 \times 10^{-6}\,^{\circ}\!C^{-1} $ and $ \alpha_z = 8 \times 10^{-6}\,^{\circ}\!C^{-1} $ along the respective edges. The block is uniformly heated to 75 °C.

(a) Calculate the new dimensions of the block.

(b) Determine the new volume (in mm³, to the nearest mm³) and the percentage increase in volume (to two decimal places).

Accepted Answer

150.075 mm, 80.048 mm, 60.024 mm; volume = 721,081 mm³; increase = 0.15%

City Guilds Model Questions Vol1 2024 Engineering Question 3

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