A hollow cylinde has an internal and external radii of 6cm and 8 cm respectively to the nearest whole number. The height of the cylinder is exactly 14 cm. Determine the exact value of internal and external radii which will give maximum volume of the material used
The volume of material used is
v = π(R^2-r^2)*h
clearly, the maximum volume is when R-r is a maximum. That is, when the cylinder wall is as thick as possible.
You have said that 5.5 < r < 6.5 and 7.5 < R < 8.5
so, r=5.5 and R=8.5 will give maximum volume