Total Surface Area of a Hollow Hemisphere?

Question

I have a problem like this on the test tomorrow but my answer is far different from the correct answer provided.

Imagine a hollowed hemisphere. The radius out the outer sphere is 1.25cm. The diameter of the inner sphere is 1.86 cm. What is the total surface area of the entire figure? (I used the (3)(pi)(r)^2 formula and added both together)

My answer: 22.86 cm2
Correct answer: 17.44 cm2

What did I do wrong?

Answer 1

The surface area of a sphere is:     A_s = 4πr²

 

So, surface area of a hemisphere is:    2πr²

 

This hemisphere is hollow.  It has a total surface area of:

      outer surface area       +      inner surface area        +      area of ring

           2π(1.25)²              +       2π(1.86/2)²          +   (  π(1.25)²  -  π(1.86/2)²  )

           3π(1.25)²       +     π(1.86/2)²

            3π(1.25)²    +  π(0.93)²

          14.71875    +   2.715786

                    17.43454

                     17.43 cm²     (rounded)

Answer 2

Surface area of a sphere=4*pi* r^2