Lista de exercícios do ensino médio para impressão
In the following picture:
$\,\overline{PP'}\,$ is the diameter of the sphere whose center is $\,O\,$, $\;M\,$ é is the center of a intersection with a plane perpendicular to $\,\overline{PP'}\,$. Also the measures are $\,\overline{AP}\,=\,6\,cm\;$ and $\,\overline{AP'}\,=\,8\,cm\;$. Calculate the area of the cicle whose center is $\,M\,$.
esfera e secção plana

 



answer: The area is $\,\frac{\,576\,\pi\;}{\;25\;}\;cm^2$
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Find the lateral area, the total area and the volume of a circular cone that is circumscribed to a sphere of radius $\,r\,$ and whose axial cut is an equilateral triangle.
sphere inscribe to a cone

 



answer: $\,S_{\text lat}\,=\,6\,\pi\,r^2\,$; $\,S_{\text total}\,=\,9\,\pi\,r^2\,$; $\,V_{\text olume}\,=\,3\,\pi\,r^3\,$
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Other math tests: sphere