# Multiple Dimensions - Volume Of a 4-Sphere

**Calculus**Level 3

Let's calculate the volume by integrating along the \( x_1 \) axis. The volume is equal to \( V(r) = \int_{-r} ^{r} A(x_1) \, d x_1 \), where \( A(x_1) \) denotes the area element for a given value of \( x_1\).

What is the area element \( A(x) \) and what is the corresponding volume \( V(r) \) of the sphere ?