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A block of stone is cut so that its cross-section is a parallelogram.

a. The width of the bottom side is greater than the width of the top side.
b. The width of the bottom side is less than the width of the top side.
c. The width of the bottom side is equal to the width of the top side.
d. The width of the bottom side depends on the length of the parallelogram.

1 Answer

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Final answer:

The volume, cross-sectional area, and height changes due to temperature changes are proportional to the original size measurements of Blocks A and B. Block B, having larger dimensions (2L x 2L x 2L), will experience a greater change in all aspects compared to Block A (L x 2L x L) when subject to the same temperature change.

Step-by-step explanation:

When considering the effects of a temperature change on two blocks, A and B, with different dimensions, we need to understand how their physical properties will adjust accordingly. Block A has dimensions L x 2L x L, while Block B is larger with dimensions 2L x 2L x 2L. Both blocks are made of the same material, so their expansion properties due to temperature changes will be similar.

Volume Change

(a) Since volume is a cubic measurement, a small change in temperature will result in a change in volume that is proportional to each block's original volume. For Block A, the volume is L x 2L x L, whereas for Block B, it is 2L x 2L x 2L. Thus, Block B will experience a greater change in volume as it has a larger original volume.

Cross-sectional Area Change

(b) The cross-sectional area (l x w) is affected by temperature changes, and since the area is proportional to the size of each side, any change will also be proportional. Block A's cross-sectional area is calculated as L x 2L, which is 2L², while Block B has a cross-sectional area of 2L x 2L or 4L². As Block B's cross-sectional area is twice that of Block A's, any change will similarly be twice as great for Block B compared to Block A.

Height Change

(c) Lastly, the change in height (h) due to temperature change will be proportional to the original height. Block B has twice the original height of Block A. Therefore, the change in height for Block B will be twice that of Block A.

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