Solid geometry, Solid figures solved problems

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. V_octahedron = ?

Geometry and use of trigonometry contents - B