Geometry - solid figures solved problems Solid figures, solved problems examples
Example:    An equilateral triangle of the side a = 6 rotates around a line parallel to its side on the distance that equals the triangle’s height (not passing through the vertex of the triangle), find the volume of the solid of revolution.
Solution:  Given a = 6.    Vsolid of revolution = ?    Vsolid of revolution = 2Vfrustum - Vcylinder   Example:   The cosine of the angle at which diagonals of a cube intersect is?
Solution:  Given a cube.   cos j = ?  Example:   In a right triangular prism inscribed is a sphere which touches all faces of the prism. The ratio of surfaces of the sphere and the prism is?
Solution:  Given a right triangular prism.    Ssphere : Sprism = ?    Ssphere = 4R2p,  Example:   In a cube inscribed is a regular tetrahedron whose edges are face’s diagonals of the cube, the ratio of volumes of the cube and the tetrahedron is?
Solution:  Given a cube.    Vcube : Vtetrahedron = ?  Example:   At what distance from the center of a not-transparent sphere of radius 4 cm should be placed the light to brighten up one third of the surface of the sphere.
Solution:  Given  r = 4 cm.    SO = ?  Example:   In an oblique circular cone the longest slant height s1= 6Ö3 and the shortest s2= 6 subtend, at the vertex of the cone, the angle of 30°, find the volume of the cone.
Solution:  Given  s1= 6Ö3 and s2= 6.    Vcone = ?  Example:   A plane passes through three vertices of a cube and cuts of it a tetrahedron. The ratio of the volumes of obtained solids is?
Solution:  Given a cube.    Vtetrahedron : (Vcube - Vtetrahedron ) = ?  Example:   Around a cone of slant height that equal the diameter of the base circumscribed is a sphere. The ratio of surfaces of the cone and the sphere is?
Solution:  Given  s = 2r.    Scone : S sphere = ?  Example:   A point source of light is 4 m distant from the center of a sphere of radius 2 m. What surface area of the sphere is brightened?
Solution:  Given  R = 2 m and  SA = 4 m.    S cap = ?     Geometry and use of trigonometry contents - B 