Geometry - solid figures solved problems
Solid figures, solved problems examples
Example:   A right triangle with legs a and b and the hypotenuse c first rotates around the leg a and then around the leg b. Find the ratio of volumes of generated solids of revolution.
Solution:  Given a and b.    Vs.r. - a : Vs.r. - b = ?
Example:   Sides of a triangle are 34, 20 and 18 cm long. Find the volume of a solid generated by rotation of the triangle around a line passing through the vertex opposite of triangles' longest side and which is parallel to it.
Solution:  Given  a = 34 cm, b = 20 cm and c = 18 cm.    Vs.r. = ?
Example:   A triangle with sides 5, 4 and 3 cm, rotates around the longest side, find the volume of the solid of revolution.
Solution:  Given  a = 5, b = 4 and c = 3.    Vs.r. = ?
Example:   An isosceles trapezium with longer base 9 cm, shorter base 5 cm and with leg 3 cm rotates around shorter base. Find the volume of the solid of revolution.
Solution:  Given  a = 9 cm, c = 5 cm and b = 3 cm.    Vs.r. = ?
Example:   An isosceles trapezium with longer base 9 cm, shorter base 1 cm and with leg 5 cm rotates around longer base. Find the surface of the solid of revolution.
Solution:  Given  a = 9 cm, c = 1 cm and b = 5 cm.    Ss.r. = ?
Example:   A rhombus with longer diagonal f and shorter diagonal e rotates around the shorter diagonal. If     ( f / 6 )2 = 1/e, find the volume of the generated solid of revolution.
Solution:  Given  ( f / 6 )2 = 1/e.    Vs.r. = ?
Example:   An isosceles triangle of the base a and the leg b, rotates around the base a. If the altitude to the base a is twice the length of the altitude to the leg b, find the surface of the solid of revolution.
Solution:  Given  a and  ha = 2hb.    Ss.r. = ?
Example:   Find the surface of a regular hexagonal pyramid whose height is four times longer than the altitude of any of six equilateral triangles that form hexagonal base.
Solution:  Given  h1 and  h = 4h1.    S = ?
Geometry and use of trigonometry contents - B