A company provides conical paper cups. Each cup has top diameter \(6.9\text{ cm}\) and height \(9.1\text{ cm}\).
Find the volume of one cup.[1]
The water dispenser has a capacity of 18.9 litres. Find the maximum number of cups that can be completely filled from one full dispenser.[2]
The company considers frustum-shaped cups. Each frustum is formed by cutting off the top portion of a similar cone so that the cut face has diameter \(6.9\text{ cm}\), equal to the top diameter of the original cone. The frustum and original cone have the same curved surface area. Find the volume of a frustum-shaped cup.[4]