Question

The side of a given cube is n units in length. If this length is tripled, how would the volume of the new cube compare to the volume of the original cube?

Answer 1

Answer:

Option 4

Step-by-step explanation:

Points to remember to solve this question,

1). Dimension scale factor of the cube = $\frac{\text{Dimension of the image}}{\text{Dimension of the original}}$

2). Volume scale factor the cube = $\frac{\text{Volume of the image}}{\text{Volume of the original}}$

3). Volume scale factor = (Dimension scale factor)³

Since, length of the cube = n units

Length of the cube after dilation = 3n units

Dimension scale factor = $\frac{3n}{n}=3$

Volume scale factor = (Dimension scale factor)³

                                  = (3)³

                                  = 27

Since, Volume scale factor the cube = $\frac{\text{Volume of the image}}{\text{Volume of the original}}$

$\frac{\text{Volume of the image}}{\text{Volume of the original}}=27$

Volume of the image cube = 27(Volume of the original cube)

Therefore, Option 4 will be the answer.