7. The temperature of a right rectangular prism of carbon steel with dimensions 70 x 130 x 10 mm is increased by 45 °C. The coefficient of linear expansion is 14 × 10-6/°C. Calculate the change in volume in mm³.
To calculate the change in volume of the right rectangular prism, we can use the formula for the volumetric expansion:
Change in Volume = Initial Volume * Coefficient of volumetric expansion * Change in Temperature
First, calculate the initial volume of the prism:
Initial Volume = length * width * height
Initial Volume = 70 mm * 130 mm * 10 mm
Initial Volume = 91,000 mm³
Now, calculate the change in volume:
Change in Temperature = 45 °C
Coefficient of volumetric expansion = 3 * (Coefficient of linear expansion)
Coefficient of volumetric expansion = 3 * 14 × 10-6/°C
Coefficient of volumetric expansion = 42 × 10-6/°C
Change in Volume = 91,000 mm³ * 42 × 10-6/°C * 45 °C
Change in Volume = 91,000 mm³ * 1.89 × 10-3
Change in Volume = 172.39 mm³
Therefore, the change in volume of the right rectangular prism is 172.39 mm³.