AnswersTX-Mathematical Models with Applications AProperties of Transformations

Properties of Transformations Answers

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1
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Make a conjecture about the similar solids. How is the scale factor and the ratio of the surface areas related? Check all that apply.

A
The dimensions of the larger cylinder are 3 times the dimensions of the smaller cylinder.
B
The surface area of the larger cylinder is 32, or 9, times the surface area of the smaller cylinder.
C
If proportional dimensional changes are made to a solid figure, then the surface area will change by the square of the scale factor of similar solids.
2
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If the radius is now 1, then the new volume is π units3.

A
2
B
4
C
8
3

Therefore, changing the height to half of its original value and changing the radius to half of its original value does the volume. Halving the height of the cone the volume, while halving the radius of the cone results in the volume.

A
not have the same effect on
B
have the same effect on
C
not change
4

Therefore, changing the height to half of its original value and changing the radius to half of its original value does the volume. Halving the height of the cone the volume, while halving the radius of the cone results in the volume.

A
doubles
B
does not change
C
halves
5

Therefore, changing the height to half of its original value and changing the radius to half of its original value does the volume. Halving the height of the cone the volume, while halving the radius of the cone results in the volume.

A
1/2
B
1/4
C
2
6

Which prism is similar to a right rectangular prism with a length of 5.2 units, a width of 2 units, and a height of 3 units?

A
Option
B
Option
C
Option
7

If the dimensions of a solid proportionally increase by a scale factor of , by what factor does the surface area increase?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

The scale factor of the larger prism to the smaller prism is . How do the volumes compare?

Question illustration
A
The volume changes by .
Option A
B
The volume changes by , or .
Option B
C
The volume changes by , or .
Option C
9

The surface areas of two similar solids are 169 m2 and 81 m2. The volume of the larger solid is 124.92 m3. Which proportion correctly shows how to solve for the volume of the smaller solid, x?

A
=
Option A
B
=
Option B
C
=
Option C
D
=
Option D
10

If the height is now 3, then the new volume is π units3.

A
4
B
8
C
12
11

Two triangular pyramids are similar. The volume of the larger pyramid is 729 cm3 , and the volume of the smaller pyramid is 64 cm3. If the perimeter of the base of the smaller pyramid is 8 cm, what is the perimeter of the base of the larger pyramid?

A
18 cm
B
18 cm2
C
27 cm
D
27 cm2
12

Which cone is similar to a right cone with a height of 3 ft and a base with a diameter of 5 ft?

A
Option
B
Option
C
Option
D
Option
13

Which properties are necessary to claim that the two prisms are congruent? Check all that apply.

A
The lengths of corresponding edges are in a 1:1 ratio.
B
The volumes are equal.
C
Corresponding angles have different measures.
D
Corresponding faces are not congruent.
E
The base areas are equal.
F
The prisms have the same height.

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