Geometry - solid figures solved problems
Solid figures, solved problems examples
Example:   Right square prism volume V = 1152 and height h = 8, find its surface area.
Solution:  Given V = 1152 and h = 8.    S = ?
Example:   Find the volume of a cube whose space diagonal length is 10Ö3.
Solution:  Given  D = 10Ö3 cm.    V = ?
Example:   The longest space diagonal of a regular hexagonal prism, d = 4 cm, if the diagonal and the lateral edge form the angle of 30°, find the volume of the prism.
Solution:  Given  d = 4 cm  and  a = 30°.    V = ?
Example:   The distance of a space diagonal of a cube of edge length a, from any of its sides, is?
Solution:  Given  a.   x = ?
Example:   A space diagonal of a rectangular prism D = 2Ö14 and its edge's lengths are in proportion a : b : c = 1 : 2 : 3, find the volume of the prism.
Solution:  Given  D = 2Ö14 and a : b : c = 1 : 2 : 3.    V = ?
Example:   The lateral edge b of length 2, of a square pyramid, is inclined to the base at the angle a = 30°.  Find the volume of the pyramid.
Solution:  Given  b = 2  and  a = 30°.    V = ?
Example:   The lateral edge of the regular hexagonal pyramid of volume V = 32 cm3 is inclined to the base at the angle 30°, find length of the side of base.
Solution:  Given  a = 30°  and  V = 32 cm3.    a = ?
Example:   Find the volume of a triangular pyramid whose all three lateral edges are of the same length and which at the vertex of the pyramid, subtend to each other, right angles.
Solution:  Given a.    V = ?
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 = ?
Geometry and use of trigonometry contents - B
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