Question

question 12: standard g.gmd.1
the pennies have the same volume due to?
image of two stacks of pennies
a. same surface areas
b. same type of material
c. equal heights and lengths
d. equal cross sectional areas and the same height

Explanation:

To determine why the pennies have the same volume, we use the concept of the volume of a cylinder (since a stack of pennies can be considered a cylinder). The volume of a cylinder is given by \( V = A \times h \), where \( A \) is the cross - sectional area and \( h \) is the height.

• Option a: Surface area is not directly related to volume in determining if two cylindrical stacks (of pennies) have the same volume. Different surface areas can exist for the same volume, so this is incorrect.
• Option b: The type of material affects density and mass, not the volume of the stack of pennies. Volume depends on the dimensions of the stack, not the material, so this is incorrect.
• Option c: Pennies are circular, so the relevant dimensions for their volume as a stack (cylinder) are cross - sectional area (related to the area of the penny) and height, not length. So this option is incorrect.
• Option d: If the cross - sectional area (area of each penny, which is the same for all pennies) is equal and the height (total height of the stack) is the same, then using the volume formula for a cylinder \( V=A\times h \), the volume will be the same. This matches the concept of Cavalieri's principle, which states that if two solids have equal heights and equal cross - sectional areas at every level, then they have the same volume.

Answer:

d. Equal cross sectional areas and the same height