Question

One hexagonal prism has dimensions that are triple the dimensions of a similar hexagonal prism. If the volume of the smaller prism is 4.75 cm3, what is the volume of the larger prism?
4.75 cm3
14.25 cm3
42.75 cm3
128.25 cm3

Answer 1

Answer:

128.25 cm3

Step-by-step explanation:

3 x 3 x 3 = 27

4.75 x 27 = 128.25 cm3

Answer 2

First, we are going to find the scaling factor of the volume, and then, we are going to multiply that scaling factor by the volume of the smaller prism.

We know that our hexagonal prism has dimensions that are triple the dimensions of a similar smaller hexagonal prism. The scaling factor for each dimension is 3, but since we have 3 dimension (a prism is a 3 dimensional figure), we need to rise that scaling factor to the power 3 (that represent the three dimensions of our prism):
$3^3=27$

Now we just need to multiply our volume scaling factor by the volume of our smaller prism:
$V=27(4.75cm^3)$
$V=128.25cm^3$

We can conclude that the correct answer is the fourth choice: 128.25 cm3