Question

Two boats labeled A and B floating on a body of water. A diagonal dashed line extends from point A through point C to point E. Another boat is at point B, directly above point C, and a vertical dashed segment connects them. A horizontal dashed segment from D to E is also perpendicular to the vertical line, forming a right angle at D. .


Given that AB¯¯¯¯¯¯¯¯ =9
units in length and BC¯¯¯¯¯¯¯¯=12
units in length, how many units is CE¯¯¯¯¯¯¯¯
?

(1 point)
Responses

15
15

6
6

24
24

21


A rectangle measures 4 inches by 10 inches. It is dilated using a scale factor of 2.5. What is the area in square inches of the dilated rectangle?(1 point)
Responses

250
250

160
160

2,500
2,500

40


Calculate and compare the surface area of sphere A
, which has a radius of 2 in
., and sphere B
, which has a radius of 10 in
. The formula for the surface area of a sphere is 4πr2
.(1 point)
Responses

Sphere A
has a surface area of 4π in.2
and sphere B
has a surface area of 100π in.2
, meaning sphere B
’s surface area is 25 times as large as sphere A
’s.
Sphere upper A has a surface area of 4 pi inches squared and sphere upper B has a surface area of 100 pi inches squared , meaning sphere upper B ’s surface area is 25 times as large as sphere upper A ’s.

Sphere A
has a surface area of 8π in.2
and sphere B
has a surface area of 40π in.2
, meaning sphere B
’s surface area is 5 times as large as sphere A
’s.
Sphere upper A has a surface area of 8 pi inches squared and sphere upper B has a surface area of 40 pi inches squared , meaning sphere upper B ’s surface area is 5 times as large as sphere upper A ’s.

Sphere A
has a surface area of 2π in.2
and sphere B
has a surface area of 10π in.2
, meaning sphere B
’s surface area is 4 times as large as sphere A
’s.
Sphere upper A has a surface area of 2 pi inches squared and sphere upper B has a surface area of 10 pi inches squared , meaning sphere upper B ’s surface area is 4 times as large as sphere upper A ’s.

Sphere A
has a surface area of 16π in.2
and sphere B
has a surface area of 400π in.2
, meaning sphere B
's surface area is 25 times as large as sphere A
’s.


A cylinder has a surface area of 54π cm2
. If it were dilated using a scale factor of 12
, what is the surface area of the new cylinder?(1 point)
Responses

108π cm2
108 pi centimetre squared

13.5π cm2
13 point 5 pi centimetre squared

27π cm2
27 pi centimetre squared

6.75π cm2
6 point 7 5 pi centimetre squared


Use the image to answer the question.

A cube with width labeled 6 centimeters, length labeled 5 centimeters, and height labeled 4 centimeters.

Imagine that a rectangular prism similar to the one shown has a scale factor of 12
. What is the volume of the new rectangular prism?

(1 point)
Responses

60 cm3
60 centimetres cubed

15 cm3
15 centimetres cubed

30 cm3
30 centimetres cubed

120 cm3
120 centimetres cubed


 Use the image to answer the question.

A right triangular prism measures 4 centimeters in width, 7 centimeters in length, and 3 centimeters in height.

If the right triangular prism is dilated using a scale factor of 3, what would be the volume of the dilated prism?

(1 point)
Responses

378 cm3
378 cm cubed

1,134 cm3
1134 cm cubed

126 cm3
126 cm cubed

2,268 cm3
2268 cm cubed
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Answer 1

Here are the answers with brief reasoning:

1) CE = 15
- 9, 12, 15 is a Pythagorean triple (√(9^2 + 12^2) = 15).

2) Area of dilated rectangle = 250 in^2
- Original area = 4×10 = 40. Scale factor 2.5 → area scale = 2.5^2 = 6.25 → 40×6.25 = 250.

3) Surface areas: Sphere A = 16π in^2, Sphere B = 400π in^2; B is 25 times A
- SA = 4πr^2 → 4π(2^2)=16π, 4π(10^2)=400π, ratio = 400/16 =25.

4) New surface area = 13.5π cm^2
- The prompt’s "scale factor of 12" appears to be a typo for 1/2. With k = 1/2, area scale = (1/2)^2 = 1/4 → 54π×1/4 = 13.5π.

5) Volume of new prism = 15 cm^3
- Original volume = 6×5×4 = 120. With scale factor 1/2 (likely intended), volume scale = (1/2)^3 = 1/8 → 120×1/8 = 15.

6) Volume of dilated triangular prism = 1,134 cm^3
- Original base area = (1/2)×4×3 = 6, original volume = 6×7 = 42. With k = 3, volume scale = 3^3 = 27 → 42×27 = 1,134.