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The right rectangular prisms are similar.
Which statements are correct? Check all that apply.
The angles in the smaller prism measure 90 degrees.
The perimeter of the rectangular bases changes by a factor of 2.
The surface area changes by a factor of 8.
The larger prism has twice the volume of the smaller prism.
The area of the rectangular bases changes by a factor of 4.
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Correct answers:
- The angles in the smaller prism measure 90 degrees.
- The perimeter of the rectangular bases changes by a factor of 2.
- The area of the rectangular bases changes by a factor of 4.
Reason: Similar right rectangular prisms keep all angles (90°). Corresponding linear measures scale by a factor k (here k = 2), so perimeters (linear) scale by k = 2, areas (including base area) by k^2 = 4, and volumes by k^3 = 8. Thus "surface area changes by a factor of 8" and "larger prism has twice the volume" are false.
- The angles in the smaller prism measure 90 degrees.
- The perimeter of the rectangular bases changes by a factor of 2.
- The area of the rectangular bases changes by a factor of 4.
Reason: Similar right rectangular prisms keep all angles (90°). Corresponding linear measures scale by a factor k (here k = 2), so perimeters (linear) scale by k = 2, areas (including base area) by k^2 = 4, and volumes by k^3 = 8. Thus "surface area changes by a factor of 8" and "larger prism has twice the volume" are false.
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