Geometry - solid figures solved problems
Solid figures, solved problems examples
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 = ?
Example:   Edges of a cuboid (rectangular prism) are in ratio 1 : 2 : 5 and length of its diagonal 5Ö6. Surface of the cuboid is?
Solution:  Given  a : b : c = 1 : 2 : 5 and D = 5Ö6 .    S rectangular prism = ?
Example:   The base of a pyramid is regular pentagon and the lateral faces are equilateral triangles. The base-to-face dihedral angle is?
Solution:  Given a regular pentagonal pyramid.    a = ?
Example:   On a horizontal surface placed are four spheres of the same radius R such that they touch each other and their centers form square. Onto these four spheres placed is the fifth sphere of the same radius which touches all the four. The distance of the center of the fifth sphere from the horizontal surface is?
Solution:  Given  R.    x = ?
Example:   An isosceles trapezoid rotates around line which passes through midpoints of its bases. If longer basis is 10 cm, shorter 6 cm and leg 4 cm, find volume and surface of generated solid of revolution.
Solution:  Given  a = 10 cm, c = 6 cm and b = 4 cm.   Vs.r. = ?  and  Ss.r. = ?
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. = ?
Geometry and use of trigonometry contents - B