Water and marbles in a boiling tube

Core stretch

A boiling tube consists of a hemisphere of radius 3 cm attached below a cylinder of the same radius and height 10 cm. Use \(\pi=3.142\).

Assume the marbles remain fully submerged and no water is lost.

1. It contains \(150\text{ cm}^3\) of water. Find
   1. the water height in the cylindrical part,[2]
   2. total depth from the tube bottom.[2]
2. Six marbles of volume \(8\text{ cm}^3\) each are immersed; find the rise.[2]
3. Find the tube’s inner surface area.[2]
4. If cylinder height increases by 10%, find the percentage increase in inner area.[2]