Lesson OVERVIEW of LESSONS on Volume of SPHERES

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OVERVIEW of LESSONS on Volume of Spheres

For your convenience,  this file contains
     - the list of my lessons on volume of spheres in this site,
     - the formula for calculating the volume of spheres,  and
     - the list of relevant solved problems.

Spheres

A  sphere  is a surface in a  3D  space all points of which are  equidistant  from one point called the  center of the sphere.
Figure 1a  shows the sphere.

A  radius of a sphere  is a straight segment connecting the center of the sphere with a point on the sphere surface  (Figure 1b).
A  diameter of a sphere  is the straight segment passing through the center of the sphere and connecting the opposite points of the sphere  (Figure 1c).

  
      Figure 1a. A sphere
          

        
          Figure 1b. A sphere
              and its radius

        
          Figure 1c. A sphere
              and its diameter


Properties of spheres


1.  Every section of a sphere by a plane is a circle.

2.  A tangent segment to a sphere released from a point in  3D  space outside the sphere is perpendicular to the radius of the sphere drawn from its center
     to the tangent point.

3.  All tangent segments to a sphere released from one fixed point outside the sphere have the same length.


Formula for calculating the volume of spheres


The volume of a sphere  is  S =  4%2F3pir%5E3 = 1%2F6pid%5E3,
where  r  is the radius of the sphere and  d  is the diameter of the sphere.


My lessons on volume of spheres in this site

    - Volume of spheres
under the topic  Volume, metric volume  of the section  Geometry,  and
    - Solved problems on volume of spheres
under the topic  Geometry  of the section  Word problems.

Solved problems on volume of spheres

    - Find the volume of a sphere if its radius is of  10 cm.
    - Find the volume of a sphere if its radius is of  3 cm.

    - Find the volume of a composite body comprised of a right circular cylinder and a hemisphere attached center-to-center                         
          to one of the cylinder bases if both the cylinder diameter and the hemisphere diameter are of  20 cm,  and the cylinder
          height is of  40 cm.
    - Find the volume of a composite body comprised of a right circular cylinder and a hemisphere attached center-to-center
          to one of the cylinder bases if both the cylinder diameter and the hemisphere diameter are of  10 cm,  and the cylinder
          height is of  20 cm.


    - Find the volume of a composite body comprised of a cone and a hemisphere attached center-to-center to the cone base                         
          if both the cone base diameter and the hemisphere diameter are of  20 cm  and the cone height is of  10 cm.
    - Find the volume of a composite body comprised of a cone and a hemisphere attached center-to-center to the cone base
          if both the cone base diameter and the hemisphere diameter are of  10 cm  and the cone height is of  5 cm.

    - Find the volume of a composite body comprised of a cube and a hemisphere attached center-to-center to one of the                              
          cube faces if both the cube edge measure and the hemisphere diameter are of  20 cm.
    - Find the volume of a composite body comprised of a cube and a hemisphere attached center-to-center to one of the
          cube faces if both the cube edge measure and the hemisphere diameter are of  10 cm.


    - Find the volume of the sphere inscribed in a cone if the base diameter of the cone is of  24 cm  and the height of the                           
          cone is of  16 cm.
    - Find the volume of the sphere inscribed in a cone if the base diameter of the cone is of  30 cm  and the height of the
          cone is of  36 cm.




My lessons on volume of spheres and other 3D solid bodies in this site are

Lessons on volume of prisms

Volume of prisms
Solved problems on volume of prisms
Overview of lessons on volume of prisms                    

Lessons on volume of pyramids

Volume of pyramids
Solved problems on volume of pyramids
Overview of lessons on volume of pyramids

Lessons on volume of cylinders

Volume of cylinders
Solved problems on volume of cylinders
Overview of lessons on volume of cylinders                

Lessons on volume of cones

Volume of cones
Solved problems on volume of cones
Overview of lessons on volume of cones                    

Lessons on volume of spheres

Volume of spheres
Solved problems on volume of spheres
Overview of lessons on volume of spheres


To navigate over all topics/lessons of the Online Geometry Textbook use this file/link  GEOMETRY - YOUR ONLINE TEXTBOOK.


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