The Sphere

Sphere is a solid bounded by closed surface every point of which is equidistant from a fixed point called the center.
 

The Right Circular Cone

Any cone with circular right section is a circular cone. Right circular cone is a circular cone whose axis is perpendicular to its base.
 

Frustum of a Right Circular Cone

Frustum of a right circular cone is that portion of right circular cone included between the base and a section parallel to the base not passing through the vertex.
 

Frustum of a Right Circular Cone

 

Frustum of a Regular Pyramid

Frustum of a regular pyramid is a portion of right regular pyramid included between the base and a section parallel to the base.
 

Frustum of a regular pyramid

 

Frustums

Frustum of a pyramid (or cone) is a portion of pyramid (or cone) included between the base and the section parallel to the base not passing through the vertex.
 

$V = \frac{1}{3}\left( A_1 + A_2 + \sqrt{A_1A_2} \right)h$

 

Frustum of a cone and frustum of a pyramid

 

The Cone

Cone
The surface generated by a moving straight line (generator) which always passes through a fixed point (vertex) and always intersects a fixed plane curve (directrix) is called conical surface. Cone is a solid bounded by a conical surface whose directrix is a closed curve, and a plane which cuts all the elements. The conical surface is the lateral area of the cone and the plane which cuts all the elements is the base of the cone.
 

Similar Figures

Two surfaces or solids are similar if any two corresponding sides or planes are proportional.
 

Solution to Problem 670 | Deflections in Simply Supported Beams

Problem 670
Determine the value of EIδ at the left end of the overhanging beam shown in Fig. P-670.
 

Overhang Beam with Triangle and Moment Loads

 

Solution to Problem 669 | Deflections in Simply Supported Beams

Problem 669
Compute the value of EIδ midway between the supports of the beam shown in Fig. P-669.
 

Overhang beam with uniform loads between supports and at the overhang

 

Solution to Problem 668 | Deflections in Simply Supported Beams

Problem 668
For the beam shown in Fig. P-668, compute the value of P that will cause the tangent to the elastic curve over support R2 to be horizontal. What will then be the value of EIδ under the 100-lb load?
 

Overhang beam with point load between supports and at the free end

 

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