Answer
$ 4 \pi $
Work Step by Step
Integrate the integral to calculate the surface area as follows:
Surface area, $S=2\pi \int_{c}^{d}(y) \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =2 \pi \int_{1}^{2} \sqrt {4y-y^2} \sqrt {\dfrac{4}{4(y-1)}}dy$
or, $=4 \pi \int_1^2 dx$
or, $= 4 \pi $
