Surface Area of Hypercylinder in d - dimensions

The volume of a hypercylinder in d-dimensions can be derived in a general way using the Cartesian product.

What is the volume of a hyper cylinder in d - dimension?

I want to find the surface area of a hypercylinder, is there an analogous way to calculate this?

The volume of a $$d$$-dimensional hyper-cylinder or radius $$r$$ and length $$h$$ is the product of the volume of a $$d-1$$-dimensional sphere times $$h$$:
$$V = \frac{r^{d-1} \pi^{(d-1)/2}}{\Gamma \left( \frac{d-1}{2}+1 \right)}h.$$
The AREA of such a cylinder is twice the surface area of an $$d-1$$-dimensional sphere (the "caps") of radius $$r$$, plus the area of a the perimeter of the $$d-1$$-dimensional sphere times $$h$$.