A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid.
For a right pyramidal frustum, let be the slant height, the height, the bottom base perimeter, the top base perimeter, the bottom area, and the top area. Then the surface area (of the sides) and volume of a pyramidal frustum are given by



(1)




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Frustum of a Cone
If a cone is cut by a plane parallel to its base, the portion of a solid between this plane and the base is known as frustum of a cone. The volume denoted by ABCD in figure is a frustum of the cone ABE.
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Volume of Frustum of a Cone:
Since, we know that cone is a limit of a pyramid therefore; frustum of a cone will be the limit of frustum of a pyramid. But volume of a pyramid is
Where
Volume of a Frustum of a Cone
A frustum may be formed from a cone with a circular base by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and an upper base that are circular and parallel.
Let h be the height, R the radius of the lower base, and r the radius of the upper base. One picture of the frustrum is the following.
Given R, r, and h, find the volume of the frustum. 
Cone (geometry)
From Wikipedia, the free encyclopedia
A right circular cone and an oblique circular cone
A cone is a threedimensional geometric shape that tapers smoothly from a flat, usually round base to a point called the apex or vertex. More precisely, it is the solid figure bounded by a plane base and the surface (called the lateral surface) formed by the locus of all straight line segments joining the apex to the perimeter of the base. The term “cone” sometimes refers just to the surface of this solid figure, or just to the lateral surface.

Volume of Cone
A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex.
The volume of a cone is given by the formula:
Volume of cone = Area of base × height
V = where r is the radius of the base and h is the height of the prism.
Pyramid (geometry)
 This article is about the polyhedron pyramid (a 3dimensional shape); for other versions including architectural pyramids, see Pyramid (disambiguation).
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base.
A pyramid with an nsided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are selfdual.

A square pyramid is a pyramid with a square base. It is a pentahedron.
The lateral edge length and slant height of a right square pyramid of side length and height are
The corresponding surface area and volume are
Prismatoid
From Wikipedia, the free encyclopedia
In geometry, a prismatoid is a polyhedron where all vertices lie in two parallel planes. (If both planes have the same number of vertices, and the lateral faces are either parallelograms or trapezoids, it is called a prismoid.)
If the areas of the two parallel faces are A_{1} and A_{3}, the crosssectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A_{2}, and the height (the distance between the two parallel faces) is h, then the volume of the prismatoid is given by (This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson’s rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.)
[edit] Prismatoid families
Families of prismatoids include:
The volume of such a solid is the same as for a prismatoid,
Cylinder (geometry)
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.
In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a oneparameter family of parallel lines. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder.


Volume of a cylinder
Surface Area of a Cylinder = 2 pi r^{ 2} + 2 pi r h
Rectangular Prism


A solid (3dimensional) object which has six faces that are rectangles.
It is a prism because it has the same crosssection along a length. 
cuboid is a boxshaped object.
It has six flat sides and all angles are right angles.
And all of its faces are rectangles.
It is also a prism because it has the same crosssection along a length. In fact it is a rectangular prism. 

Volume and Surface Area
The volume is found using the formula:
Volume = Height × Width × Length
Which is usually shortened to:
V = h × w × l
Or more simply:
V = hwl
Surface Area
And the surface area is found using the formula:
A = 2wl + 2lh + 2hw
Cube
From Wikipedia, the free encyclopedia
In geometry, a cube^{[1]} is a threedimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry).
A cube is the threedimensional case of the more general concept of a hypercube.
It has 11 nets.^{[2]} If one were to colour the cube so that no two adjacent faces had the same colour, one would need 3 colours.
If the original cube has edge length 1, its dual octahedron has edge length .
A cube is a threedimensional figure with six matching square sides.
The figure above shows a cube. The dotted lines indicate edges hidden from your view.
If s is the length of one of its sides, the
Volume of the cube = s^{3}
Since the cube has six squareshape sides, the
Surface area of a cube = 6s^{2}

