Mathematics
A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 metres and its volume is of the hemisphere. Calculate the height of the cone and the surface area of the buoy correct to 2 places of decimal.
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Answer
The figure of the buoy made by surmounting a right cone on a hemisphere is shown below:
Radius of base of hemisphere = Radius of cone = 3.5 m.
Volume of hemisphere (V) =
Putting values,
Volume of cone = Volume of hemisphere.
∴ Volume of cone =
Volume of cone = .
Slant height of cone = l =
Putting values we get,
Surface area of the buoy = Curved Surface area of cone + Curved Surface area of hemisphere = πrl + 2πr2.
∴ Surface area of buoy =
Hence, the height of cone = 4.67 m and surface area of buoy is 141.17 m2.
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