Gce Model Questions Vol1 2017 Mathematics Question 33

A cylindrical tank has radius \(2\) m and height \(6\) m. It is filled with water to a depth of one‑third of its height. A conical frustum with the same base radius \(2\) m, top radius \(1\) m and height \(3\) m is placed on top of the tank, its larger base coinciding with the tank's top. (a) Find the total volume of water required to fill the combined container up to the top of the frustum, expressing your answer in exact form and to three decimal places (cubic metres). (b) Find the total internal surface area of the container that is in contact with the water (including the bottom of the cylinder, the cylindrical side up to the water level, and the lateral surface of the frustum), giving your answer in exact form and to two decimal places (square metres).