Jordan Measurable set

Question

Ok so I need to demonstrate that the set $A = B(x,r) = \{x \in \mathbb{R}^d | |x|<r\}$ is a Jordan measurable set.

My attempt was to make use of the property which says that a set $A$ is a Jordan measurable set if $\forall \epsilon >0 $ there are two elementary sets $E,F$ such that $E \subset A \subset F$ such that the measure of the set $F-E$ is less then $\epsilon$

So I tryied to construct the sets $E,F$ like this: $F = [0-r,0+r] \times [0-r,0+r] \times ... \times [0-r,0+r] \in \mathbb{R}^d$, and $E = [0-r+\epsilon,0+r+\epsilon] \times[0-r+\epsilon,0+r+\epsilon] \times ... \times [0-r+\epsilon,0+r+\epsilon]\in \mathbb{R}^d $
The first contition is meet (i.e. $E \subset A \subset F$). Now I need to find the measure of $F-E$.
The set $F-E$ I believe is the set $[-\epsilon, \epsilon] \times [-\epsilon, \epsilon]\times... \times [-\epsilon, \epsilon]$, and its measure is $2d\epsilon$
And from here I stuck. I don't know If my solution is good at all. Also I need to find the measure of that set.