A buoy carrying a beacon light has the upper portion cylindrical with a $2$ m diameter and a depth of $1\mathrm{.}25$ m $.$ The lower portion which is curved, displaces a volume of $400$ liters and its center of buoyancy is situated $1\mathrm{.}3$ m below the top of the cylinder. The center of gravity of the whole buoy and beacon is situated $0\mathrm{.}95$ m below the top of the cylinder and total displacement is $2\mathrm{.}6$ tonnes. Find the meta$-$centric height. Take the specific mass of sea water $1020k\frac{g}{m}3.$

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