Gel-filled cylindrical sensor housing

A sealed water-quality sensor is externally a cylinder of radius 4 cm and height 10 cm. Its internal gel chamber is a cylinder of radius 2.5 cm and height 10 cm, reduced by a hemispherical sensor recess of radius 2.5 cm at its base. Use \(\pi=3.142\) and give decimal answers to 2 d.p.

1. The exposed lower face is the outer annulus plus the curved recess. Find its area.
2. 1. The chamber is filled to 90% of its usable capacity. Find the gel volume.
   2. The sealed sensor has mass 400 g. Using its external displaced volume, determine whether it floats in saline of density \(1.03\text{ g/cm}^3\).