MOI Physics

Problem:
Consider an ice skater spinning in a circle. We will approximate the body as a cylinder with a radius of 0.25 m. The total mass of the skater is 50kg. When the skater has her arms extended we will approximate her body as a cylinder with two rods attached. Each arm is 0.75 m long and has a mass of 2.5 kg. When the skater brings her arms in, we will approximate her body as a cylinder.

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Questions:
a)What is the moment of inertia of one of the skater's arms?

b)What is the total moment of inertia of the skater with her arms outstretched?

c)What is the total moment of inertia of the skater after she brings in her arms?

d)When the arms are extended, the skater spins at a rate of 5 rad/s. What is the angular velocity of the skater when she brings in her arms?

e)How does the skaters energy increase from when her arms are extended to when they are compressed- where is the energy coming from?

Attempt:
a)It says to use the parallel axis theorem I=Icm+md^2, but I didn't know how to apply it, so I did
I=1/2(MR^2)+(2.5kg)(0,525)^2
=1.40625+0.689 ~ 2.095 kg/m^2

b)I=1.40625+2(0.689)~2.784 kg/m

c)I=1/2(MR^2)
=1/2(50)(0.25^2)
=1.563 kg/m^2

d)IoWo=IW
(2.784*5rad)/1.563=W
W=8.9 rad/s

e)I was able to determine that there is an increase in the skater's energy, but I need to figure out where the energy is coming from.

I am apparently supposed to use the parallel axis theorem I= Icom+ md^2
for part a. How would i do this; what equation would i set up.

I know that, for the arm, im supposed to use ml^2/12 but how would I set it up