Solenoid and magnetism help?

Got this question and I think I have the right answer, but the answer isn't in the back so I can't check.

A solenoid 10.0cm in diameter and 75.0cm long is made from copper wire of diameter 0.100 cm, with very thin insulation. The wire is wound onto a cardboard tube in a single layer, with adjacent turns touching each other. What power must be delivered to the solenoid if it is to produce a field of 8.00 mT at its center?

I know that:

B = μ₀nI, where B is the magnetic field, μ₀ is the permeability of free space (4πx10⁻⁷), n is the number of turns per unit length, and I is the current.

So to find N, the number of coils in the length, I did:

75.0 cm / 0.100 cm = 750 coils.

Therefore n, coils per unit length, is:

750 coils / 75cm = 10 coils / cm = 1000 coils / m

So:

I = B / (μ₀n) = 0.008 T / (μ₀(1000)) ≈ 6.367 A

P = I²R and copper has a resistivity of 1.7x10⁻⁸.

1000 coils / m at 10cm for each coil works out to:

C = dπ = .1π m

Length = C*N = .1π(1000) = 100π m ≈ 314.16 m

P = (6.367A)²(1.17x10⁻⁸ ohm*m) / (314.16 m) = 1.5x10⁻⁹ W

Just want to know if my answer is correct and my methods are correct. Not much an application of math kinda guy. I'm definitely more comfortable with abstract concepts.

Thanks!