Question 132195
You agree the volume of this is the cross sectional area times the height, so the real task is to find the cross sectional area.

Draw a circle and on it add a chord of length 10 (the barn wall). Do you agree that the area we want is the major segment defined by this chord?

We know the perpendicular distance from the center to the chord is 5, therefore we can calculate the radius of the circle and the angle defining the relevant sector. 

I think you know where to go from here, but if not, you basically say the area of the major segment is the total area minus the area of the minor segment. The area of the minor segment is the area of the sector minus the area of the triangle.