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.<…

Question

asked Dec 19, 2018 43.0k views

2 Answers

SvenG · Answer 1 · 2018-12-26T13:42:23+0000

Answer:

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.