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

Volume of the new cube is
`{2.5^(3)` times larger than the original cube.

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 =
`((2.5x)^(3))/(x^(3))`

i.e. Factor =
`(2.5^(3)* 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.