Question

A cube is dilated by a factor of 2.5.

How many times larger is the volume of the resulting cube than the volume of the original cube?



Enter your answer as a decimal in the box.

Answer 1

It should be 2.5³
Which should equal to 15.625

Answer 2

Answer:

$(2.5)^{3}$

Step-by-step explanation:

Given : A cube is dilated by a factor of 2.5.

To Find: How many times larger is the volume of the resulting cube than the volume of the original cube?

Solution :

Let the length of the sides of the original cube = x units.

Formula of volume of cube $=a^{3}$

Where a is the side of cube

So, Volume of the original cube$=x^{3}$

Since we are given that the original cube is dilated by a factor of 2.5

So, the length of the side of the dilated  cube will be '2.5x' units.

Thus, Volume of the new cube $=(2.5x)^{3}$                                                

The factor by which volume of the new cube is larger than the volume of the original cube is:

Factor = $\frac{(2.5x)^{3}}{x^{3}}$

Factor = $\frac{(2.5)^{3}*x^{3}}{x^{3}}$

Factor = $(2.5)^{3}$

Hence the volume of the new cube is $(2.5)^{3}$ of the original cube

i.e. Factor =

i.e. Factor =

Hence, the volume of the new cube is  times larger than the original cube.