i) $\to$ b) $\to$ 1), iii) $\to$ a) $\to$ 2).

i) $\to$ b) $\to$ 3), ii) $\to$ c) $\to$ 1).

ii) $\to$ c) $\to$ 1), iii) $\to$ a) $\to$ 2).

i) $\to$ b) $\to$ 1), ii) $\to$ c) $\to$ 3), iii) $\to$ a) $\to$ 2).

The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=R$.

The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=\sqrt{3}R$.

The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=\genfrac{}{}{0ex}{}{R}{\sqrt{3}}$.

The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=2R$.

The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\genfrac{}{}{0ex}{}{R}{\sqrt{2}}$.

The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\sqrt{2}$.

The error in prediction for company A is $\genfrac{}{}{0ex}{}{5}{12}$.

The error in prediction for company A is $\genfrac{}{}{0ex}{}{11}{12}$.