Question

A pentagonal pyramid has a volume of 1536 in3. What is the volume of the pentagonal pyramid if the measures are multiplied by ?

A. 384 in3
B. 128 in3
C. 96 in3
D. 24 in3

The volume of a cube is 512 cm3. What are the sides multiplied by if the original volume of the cube was 8 cm3?

A. 4
B. 1/4
C. 64
D. 1/64
What are the sides of a rectangular prism increased by if the volume increases from 54 mm3 to 3456 mm3?

A. 2
B. 3
C. 4
D. 5


What is the volume of a rectangular prism when the lengths are tripled? L=5 W=4 H=3


A. 1620 ft3
B. 810 ft3
C. 360 ft3
D. 180 ft3

The radius and height of the cylinder are multiplied by 3. What is the volume of the cylinder?
radius =2 height =5

A. 540π in3
B. 360π in3
C. 180π in3
D. 60π in3

Answer 1

1. A
2. C
3. C
4. B
5. D

Im not 100% sure but I tried my best :) good luck.

Answer 2

The first question is incomplete.

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Question 2:

The volume of a cube is 512 cm³

512 cm³ = 8 cm x 8 cm x 8 cm or sides of 8 cm

8 cm³ = 2 cm x 2 cm x 2 cm or sides of 2 cm

So each side got multiplied by:

`(8)/(2)=4` times.

Option A is the answer.

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Question 3.

The scale factor can be derived by :

`k^(3) =(3456)/(54)`

`k^(3) =64`

`k=\sqrt[3]{64}`

k = 4

Hence, the sides of a rectangular prism increased by 4.

Option C is the answer.

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Question 4.

The original volume is given by =
`5*4*3=60` cubic feet

So, when the lengths are tripled, the overall volume is:

So, this can be shown as :

`(5*3)(4*3)(3*3)=1620` cubic feet

Option A is the answer.

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Question 5.

The given radius and height are 2 units and 5 units respectively.

Also given, the radius and height of the cylinder are multiplied by 3, so new radius ad height becomes: 6 units and 15 units respectively.

Now, volume of cylinder is given as :

V =
`\pi r^(2) h`

So, the answer will be = V =
`\pi* 6^(2)* 15`

= 540π cubic units

Option A is the answer.

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