Geometry - solid figures solved problems
      Solid figures, solved problems examples
Example:   The midpoint of the altitude of a tetrahedron of the edge a is connected with all three vertices of the base, find the angle these connections make.
Solution:  Given  a.    a = ?
 
Example:   Given is a cube of edge a. Midpoints of its faces are vertices of a regular octahedron. Find the volume of the octahedron.
Solution:  Given  a.    Voctahedron = ?
 
Example:   By rolling the cone about its apex obtained is lateral surface area of a cone in a form of a semicircle of radius R = 23 m. Find the volume of the cone.
Solution:  Given  R = 23 m.    Vcone = ?
Example:   Volume of a circular cone is V. Through the midpoint of the altitude of the cone passes a plane parallel to the base of the cone, find the volume of the part of the cone between base and the plane.
Solution:  Given  V.   Vconical frustum = ?
 
Example:   In a cone of base B and the height h inscribed is a cone with the vertex at the center of the given cone and whose height is half of the given cone. Find the volume of the inscribed cone.
Solution:  Given B and h.    Vinscribed cone = ?
 
Example:   An isosceles triangle, of leg b = 2 that is inclined to the base at a = 30, rotates around its base bisector. Find the volume of obtained solid of revolution.
Solution:  Given  b = 2 and a = 30.    Vsolid of revolution = ?
 
Example:   Find the volume of the solid generated by rotating an equilateral triangle ABC of the side a = 2 around the axis which passes through vertex C parallel to base AB
Solution:  Given a = 2.   Vsolid of revolution = ?
 
Example:   In a regular square pyramid of height 2 and side of the base 1 inscribed is a cube. The side of the cube is? 
Solution:  Given  h = 2 and  a = 1.    x = ?
 
Example:   Height of a cone is 12 and the volume 324p. Find the central angle of the sector to which is unrolled the side surface of the cone.
Solution:  Given  h = 12 and  V = 324p.    a =  ?
 
Geometry and use of trigonometry contents - B
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