Question

the side length of a cube can be represented by the expression 2x^5. if the side length is doubled, write an expression to represent the new volume of the cube

Answer 1

If the side length of a cube is multiplied by a ratio k, the volume is multiplied by the ratio k³.

Here the side length is multiplied by 2, therefore the new volume
= old volume * 2³
= 2x^5 * 8
= 16x^5.

Answer 2

The expression that represents the new volume of the cube is 64x³⁰

The formula for calculating the volume of a cube is expressed as:

Volume of cube = s³

If the side length of 2x⁵ is doubled, hence the side length of the new cube will be (2x⁵)² = 4x¹⁰

Get the new volume as shown:

$V = (4x^{10})^3\\V = 4^3(x^{10})^3\\V =64x^{30}$

This shows that expression that represents the new volume of the cube is 64x³⁰

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