Answer
$226.195 \space mm^3$
Work Step by Step
Our aim is to integrate the integral to compute the surface area. In order to solve the integral, we have:
$Surface \space Area(S_A)= (2 \pi)\int_{a}^{b} y \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =(2 \pi)\int_{7}^{16} \sqrt {256-x^2} \times \dfrac{256}{256-x^2} dx $ or, $ =[32 \pi x ]_{7}^{16}$
or, $ \approx 904.779$
The volume for each color is:
$(904.779) \times (0.05 \space mm) = 45.2389 mm^3$
The required amount of liters of each color is $226.195 \space mm^3$
