First, we need to find the volume of the filling.
The volume of a cylinder with a hemispherical top can be calculated by finding the volume of the cylinder and adding half the volume of the sphere on top.
Volume of cylinder = πr^2h
Volume of cylinder = π(1)^2(3) = 3π mm^3
Volume of hemisphere = (2/3)πr^3
Volume of hemisphere = (2/3)π(1)^3 = (2/3)π mm^3
Total volume = Volume of cylinder + Volume of hemisphere
Total volume = 3π + (2/3)π
Total volume = (11/3)π mm^3
Now, we can calculate how much the gold filling costs.
Cost of the filling = Volume of the filling x Cost per cubic millimeter
Cost of the filling = (11/3)π x $91
Cost of the filling = (11/3) x 3.14 x $91
Cost of the filling ≈ $1043.73
Therefore, the gold filling would cost approximately $1043.73.
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.
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