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Solid Geometry

Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids.

Cubes
A cube is a three-dimensional 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 x s x s.

Since the cube has six square-shape sides,

the Surface area of a cube = 6 x s x s

Cuboid

In a cuboid, the length, width and height may be of different lengths.

The volume of the above cuboid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
Surface area of rectangular solid = 2(lw + wh + lh)

Prisms
A prism is a solid that has two congruent parallel bases that are polygons. The polygons form the bases of the prism and the length of the edge joining the two bases is called the height.

A rectangular solid is a prism with a rectangle-shaped base.
The volume of a prism is given by the product of the area of its base and its height.

Cylinders
A cylinder is a solid with two congruent circles joined by a curved surface.
In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height.

Spheres
A sphere is a solid with all its points the same distance from the center.

Cones

A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of its base is perpendicular to the base.

Pyramids
A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles.