How do I solve for the volume of this prism? ?

The same as any other prism:  Find the area of the base and multiply it by the height.

In this case, instead of a full circle, you have a wedge taken out of it.  So we'll start by finding the area of the full circle and use ratios to find the area of what hasn't been removed.

A = πr²

A = π(8.4)²

A = 70.56π

That's the area for the full 360 degrees.  Since there are 50 degrees cut out of this, we have 310 degrees left.  Use ratios and proportions to find the area of what's left:

70.56π/360 = x/310

360x = 21873.6π

x = 60.76π

That's the area of the base.  Now we can multiply that by the length and that's the volume:

60.76π * 70.5 = 4283.58π cm³

Area of the base  (the circular sector)  X length

   A = (310/360)  X pi X 8.4^2 

   V = A X 70.5

  V = 13457.26346cm^3