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Solid Geometry

Solid Geometry is the geometry of three-dimensional space and concerned with the properties of 3D geometric figures like cube, cuboid, sphere, cylinder and pyramid. Solid shapes deal with three coordinates like x-coordinate, y-coordinate and z-coordinate and can not be drawn on a sheet of paper. Three dimensional shapes are solid or hollow. Shapes shown below have three dimensions: length, breadth and height. Solid geometry figures are classified by count the number of edges, faces and vertices.

Solid Shapes
Properties of some solid figures:

  • Cube has 6 square faces, 8 vertices and 12 edges.
  • Cuboid is a shape which has six rectangular faces, 8 vertices and 12 edges. 
  • Sphere is a round shape, has only one curved face.
  • Hemisphere is half of a sphere.
  • Cylinder is a figure with equal circular ends.
  • Cone is a shape with a circle at its base and pointed vertex.
  • A prism is a polyhedron with two parallel and congruent polygonal bases.
Below are some formulas used in Solid Geometry to calculate surface area and volume of the solid figures.

Formulas for Solids

Let us see with the help of example how to use above mentioned formulas:

Example: Find the volume and surface area of a sphere with radius 4. (Use $\pi$ = 3.14)

Solution:  Radius of a sphere (r) = 4

Volume of sphere = $\frac{4}{3}$ $\pi$ r$^3$

= $\frac{4}{3}$ $\times$ 3.14 $\times$ 4$^3$

= $\frac{4}{3}$ $\times$ 3.14 $\times$ 64

= 267.94

Surface area of sphere = 4$\pi$ r$^2$

= 4 $\times$ 3.14 $\times$ 16

= 200.96

$\therefore$ The volume of the sphere = 267.94 cubic units
Surface area of sphere = 200.96 sq. units.

Related Calculators
Calculate Geometry

More topics in  Solid Geometry
Cube Cuboid
Pyramid Sphere
Cylinder Cone
Prism Tetrahedron
Parallelepiped Volume of Hemisphere and Sphere
Eccentricity of Ellipse
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