Answer
$226.195 \space mm^3$
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2} =2 \pi \times \int_{7}^{16} \sqrt {256-x^2} \times \dfrac{256}{256-x^2} dx = 904.779$
Now, the volume for each color is equal to:
$(904.779) \times (0.05 \space mm) = 45.2389 mm^3$
and we multiply by $5000$ to find total woks, that is,
$5000 \times ( 45.2389 mm^3) =226,195 \space mm^3$
Thus, the required amount of liters of each color is equal to:
$\dfrac{226,195 \space mm^3}{1000} \approx 226.195 \space mm^3$
