Question

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.

Explanation:

Step1: Analyze angle property

Right rectangular prisms have all angles as 90 degrees, so smaller prism angles are 90° (correct).

Step2: Find scale factor

Larger prism dimensions: \(2.2, 0.8, 3.2\); Smaller: \(1.1, 0.4, 1.6\). Scale factor \(k=\frac{2.2}{1.1}=2\) (or \(\frac{0.8}{0.4}=2\), \(\frac{3.2}{1.6}=2\)).

Step3: Perimeter of bases

Perimeter is linear, so scale factor for perimeter is \(k = 2\) (correct).

Step4: Surface area scale

Surface area scale factor is \(k^2=2^2 = 4\), not 8 (incorrect).

Step5: Volume scale

Volume scale factor is \(k^3=2^3 = 8\), so larger volume is 8x smaller, not 2x (incorrect).

Step6: Base area scale

Base area (2D) scale factor is \(k^2=4\) (correct).

Answer:

• 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.