Inverse trig function help?

V = (1/3)(pi)(r^2)(h) = 10 in^3

We know everything in this equation EXCEPT for the height, so solve for it:

h = 3V / (pi)(r^2) = 3(10in^3) / (pi)(4in^2) = 15 /2(pi) inches

now, slicing the cone right down the middle, from the tip to the base, we have a right triangle.

If you draw this it is much more clear.

So, we have that one side of the triangle is 15 / 2(pi) inches and the other side is r/2 = 1 inch

If you remember that tangent is "opposite over adjacent" then we can solve for this angle

tan^-1(1 / (15 / 2(pi))) = 22.73 degrees

BUT, if you remember we cut the cone in half so that we could use properties of a right triangle.

To arrive at the answer we must multiply this angle by 2

Therefore we have,

β = 2*22.73 = 45.46 degrees

Hope this helps