Question

The right rectangular prisms are similar. The bigger prism has a length of 2.2, width of .8, and height of 3.2. The smaller prism has a length of 1.1, width of .4, and height of 1.6.
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.

Answer 1

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.

Step-by-step explanation:

Two polygons are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.

A) Since the two prism are similar, therefore they are to have the same angle measure. The bigger prism has angles with measure of 90°, hence the angles in the smaller prism will also measure 90.

 

B) Perimeter of bigger prism base = 2(2.2 + 0.8) = 6

Perimeter of smaller prism base = 2(1.1 + 0.4) = 3

Hence, The perimeter of the rectangular bases changes by a factor of 2 (6 / 3).

 

C) Surface area of bigger prism = 2(2.2*0.8 + 3.2*0.8 + 3.2*2.2) = 22.72

Surface area of smaller prism = 2(1.1*0.4 + 1.6*0.4 + 1.6*1.1) = 5.68

22.72 / 5.68 ≠ 8, hence the surface area does not change by a factor of 8

Option C is wrong

D) Volume of bigger prism = 3.2 * 2.2 * 0.8 = 5.632

Volume of smaller prism = 0.4 * 1.6 * 1.1 = 0.704

The volume of larger prism is not twice of the smaller prism (5.732 / 0.704 ≠ 2)

 

E) Area of bigger prism base = 2.2*0.8 = 1.76

Area of smaller prism base = 2.2*0.8 = 0.44

Since 1.76 / 0.44 = 4; The area of the rectangular bases changes by a factor of 4