Question

In measuring the volume of the​ object, when you reduce the length of your ruler by a factor of 8​, the number of volume elements increases by a factor of 512 what's the dimension

Answer 1

3

Explanation:

we know that

In this problem we can use this equation:

`N=R^(D)`

Where:

N is the increase factor

R is the reduce factor

D is the dimension

we have

`N=512\\R=8`

substitute the given values

`512=8^(D)`

solve for D

Apply log both sides

`log(512)=log(8^(D))`

Apply property of logarithms

`log(512)=(D)log(8)`

`D=log(512)/log(8)=3`

therefore

The dimension is 3