Lesson OVERVIEW of LESSONS on Surface Area of SPHERES

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OVERVIEW of LESSONS on Surface Area of Spheres

For your convenience,  this file contains
     - the list of my lessons on surface area of spheres in this site,
     - the formula for calculating the surface area 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 surface area of spheres


The surface area of a sphere  is  S =  4pir%5E2 = pid%5E2,
where  r  is the radius of the sphere and  d  is the diameter of the sphere.


My lessons on surface area of spheres in this site

    - Surface area of spheres
under the topic  Area and surface area  of the section  Geometry,  and
    - Solved problems on surface area of spheres
under the topic  Geometry  of the section  Word problems.

Solved problems on surface area of spheres

    - Find the surface area of a sphere if its radius is of  10 cm.
    - Find the surface area of a sphere if its radius is of  5 cm.

    - Find the surface area 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 surface area 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 surface area 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  20 cm.
    - Find the surface area 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  10 cm.

    - Find the surface area 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 surface area 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 surface area 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 surface area of the sphere inscribed in a cone if the base diameter of the cone is of  80 cm  and the height of the
          cone is of  75 cm.




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

Lessons on surface area of prisms

Surface area of prisms
Solved problems on surface area of prisms
Overview of lessons on surface area of prisms                  

Lessons on surface area of pyramids

Surface area of pyramids
Solved problems on surface area of pyramids
Overview of lessons on surface area of pyramids

Lessons on surface area of cylinders

Surface area of cylinders
Solved problems on surface area of cylinders
Overview of lessons on surface area of cylinders              

Lessons on surface area of cones

Surface area of cones
Solved problems on surface area of cones
Overview of lessons on surface area of cones                

Lessons on surface area of spheres

Surface area of spheres
Solved problems on surface area of spheres
Overview of lessons on surface area 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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