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 will be turned into 2.5³ which would then equal to 15.625

Answer 2

Answer:

Volume of the new cube is ${2.5^{3}$ times larger than the original cube.

Step-by-step explanation:

We are given that,

A cube is dilated by a factor of 2.5.

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

Thus, we have,

Volume of the original cube = $side^{3}$

i.e. Volume of the original cube = $x^{3}$

Now, as the original cube is dilated by a factor of 2.5

Then, the length of the sides of the new cube will be '2.5x' units.

Thus, Volume of the new cube = $side^{3}$

i.e. Volume of the new cube = $(2.5x)^{3}$

So, the factor by which volume of the new cube is larger than the volume of the original cube is,

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

i.e. Factor = $\frac{2.5^{3}\times x^{3}}{x^{3}}$

i.e. Factor = ${2.5^{3}$

Hence, the volume of the new cube is ${2.5^{3}$ times larger than the original cube.