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The volume of the dish, the amount of liquid it could hold if the rim were horizontal and the vertex at the bottom, is given by <math>\scriptstyle V= \frac {1} {8 F}\pi R^4 ,</math> or equivalently <math>\scriptstyle V=2\pi F D^2,</math> or <math>\scriptstyle V= \frac {1} {2} \pi R^2 D ,</math> where the symbols are defined as above. This last version can be compared with the well-known formulae for the volumes of a cylinder and a cone. Of course, <math>\scriptstyle \pi R^2 </math> is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight the reflector dish can intercept. | The volume of the dish, the amount of liquid it could hold if the rim were horizontal and the vertex at the bottom, is given by <math>\scriptstyle V= \frac {1} {8 F}\pi R^4 ,</math> or equivalently <math>\scriptstyle V=2\pi F D^2,</math> or <math>\scriptstyle V= \frac {1} {2} \pi R^2 D ,</math> where the symbols are defined as above. This last version can be compared with the well-known formulae for the volumes of a cylinder and a cone. Of course, <math>\scriptstyle \pi R^2 </math> is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight the reflector dish can intercept. | ||
The surface area of a paraboloidal dish can be found using the area formula for a surface of revolution, which gives <math>\scriptstyle A=\frac{\pi R}{6 D^2}\left((R^2+4D^2)^{3/2}-R^3\right) | The surface area of a paraboloidal dish can be found using the area formula for a surface of revolution, which gives <math>\scriptstyle A=\frac{\pi R}{6 D^2}\left((R^2+4D^2)^{3/2}-R^3\right)</math>. | ||
=== Paraboloids made by rotating liquids === | === Paraboloids made by rotating liquids === | ||