A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a​ patient's tooth. The radius r of the filling is 1 mm. The height of the cylinder is 3 mm. Find the volume of the filling. If dental gold costs ​$91 per cubic​ millimeter, how much did the gold cost for the​ filling? Use 3.14 for pi.

The volume of the filling is
  
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1 answer

The volume of the filling can be found by adding the volume of the cylinder and the volume of the hemisphere.

Volume of cylinder = πr^2h = 3.14 * 1^2 * 3 = 9.42 mm^3
Volume of hemisphere = 2/3 * πr^3 = 2/3 * 3.14 * 1^3 = 2.09 mm^3

Total volume = Volume of cylinder + Volume of hemisphere
Total volume = 9.42 + 2.09 = 11.51 mm^3

The cost of the gold filling can be found by multiplying the volume by the cost per cubic millimeter.

Cost = 11.51 * $91 = $1048.41

Therefore, the gold filling cost $1048.41.