A cube has side length a . The side lengths are decreased to 20% of their original size. Write an expression in simplest form for the volume of the new cube in terms of a .

Given a cube of length, a, then when decreased by 20%, what's left is actually 80% of the original. So, for this case, we have a cube with a length of 80%(a) = 0.80a.

Now, to compute for the volume of a cube, we multiply the length three times to itself. Or, in other words, raise the length to the third power. That means the volume of the new cube is (0.8a)³ = 0.512a³ cubic units.

Answer: 0.512a³ cubic units

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aksnkj aksnkj · Answer 2 · 2022-03-01T07:46:38+01:00

The expression for the volume of the cube after reduction of the side by 20% is [tex]V'=0.512a^3[/tex].

Let the side of the cube be a.

It is given that the length of the side of the cube is reduced by 20%.

What is the formula for the volume of the cube?

The volume of the cube of side a can be written as,

[tex]V=a^3[/tex]

After the reduction of length of side by 20%, the new volume of the cube will be,

[tex]V'=(a')^3\\V'=(a-20\% \times a)^3\\V'=(a-0.2a)^3\\V'=(0.8)^3\\V'=0.512a^3[/tex]

Therefore, the expression for the volume of the cube after reduction of the side by 20% is [tex]V'=0.512a^3[/tex].

To learn more about the volume of a cube, refer to the link:

https://brainly.com/question/1972490