Final answer:
The volume of rectangular blocks and their changes with temperature are governed by simple geometric formulas. Block A's volume is 2L³ and Block B's is 8L³. Changes in volume, cross-sectional area, and height due to temperature are proportional to their respective original dimensions.
Step-by-step explanation:
The question involves the concept of the volume of geometric figures, specifically rectangular blocks, and how their volumes change with temperature in the context of Mathematics. To find the volume of any rectangular piece, you use the formula volume = length × width × height. For the blocks in question, Block A, which has dimensions L × 2L × L, would have a volume of 2L³, and Block B, with dimensions 2L × 2L × 2L, would have a volume of 8L³.
(a) Since the change in volume is proportional to the original volume and, given that Block B's volume is four times that of Block A, the change in volume of Block B will be four times that of Block A when the temperature changes. (b) The cross-sectional area of Block A is the product of L and 2L, which is 2L², and for Block B, it is the product of 2L and 2L, which is 4L². Therefore, the change in cross-sectional area due to temperature will also be dependent on the material's properties but is directly proportional to the original cross-sectional area. (c) The change in height will depend on the coefficient of thermal expansion of the material and the temperature change but is directly proportional to the original height.