Solid figures
Solid figures are objects in threedimensional space. That means they have width, length and height. There are many kinds of solid figures, but the basic types are: spheres, prisms, cylinders, pyramids and cones. They have several components – faces, edges and a base. Faces are the flat surfaces on the solid figure. They can be in different shapes – circles, triangles, rectangles and squares. The only solid figures that do not have faces are spheres.
Bases are sides and polygons by which the figure is named and edges are the line segments where two segments of a solid figure meet. We will now describe to you the kinds you will encounter most often.
Spheres
Spheres are perfectly round threedimensional geometrical objects. It is completely symmetrical around its center, which means that all points on its surface are equally distant from its center. Since it resembles a circle in any twodimensional perspective, it shares some of its elements. As the circle, it also has a radius and a diameter. The radius (r ) is the distance from the center of the sphere to any point on its surface, while the diameter (d ) is the maximum straight distance through the sphere. It is also the only object without any straight surfaces.
In this phase of your education, you will have to know two things about spheres: how to calculate the volume of a sphere and how to determine the size of its surface area.
The volume of a sphere (V ) can be easily calculated by inserting the known radius of the sphere into this formula:
V = (4/3) * π * r^{3}
The surface area of a sphere (A ) is calculated in a similar way, using this formula:
A = 4 * π * r^{2}
Cylinders
Basically, a cylinder is an object whose surface is defined as being formed by the points that are at a fixed length from the imaginary axis that passes through the center of the two parallel circles which make the faces of the cylinder.
Cylinders have two circles for faces, one of them is a base. Its volume can be is calculated as the product of the surface of one of its bases and the height of the cylinder. The formula for this is:
V = π * h * r^{2}
The surface area of a cylinder can be calculated using this equation:
A = 2 * π *r * (r+h)
Prisms
A prism is a polyhedron ( a threedimensional solid) , a geometric solid with flat faces and straight sides. There are many kinds of prisms and they are mostly named with respect to the shape of its base. They can be triangular prisms ( a triangle as a base), rectangular, square prisms, pentagonal, hexagonal and so on.
Its volume can be calculated using the equation:
V = B * h
The surface area though depends on the type of prism. If it is a right prism, then the formula goes like this:
A = 2 * B + P * h
This is the basic information about the basic solid figures. There are very many of them and soon we hope to add most of them in the archive of this site. In the mean time, you can practice what you learned about solid figures so far with the help of our free math worksheets below.
Solid figures exams for teachers
Exam Name  File Size  Downloads  Upload date 
Prism


Solid figures – Prism – very easy  620.9 kB  2473  October 13, 2012 
Solid figures – Prism – easy  455.8 kB  2022  October 13, 2012 
Solid figures – Prism – medium  456.2 kB  2120  October 13, 2012 
Solid figures – Prism – hard  716.1 kB  1287  October 13, 2012 
Solid figures – Prism – very hard  702.6 kB  1171  October 13, 2012 
Pyramid


Solid figures – Pyramid – very easy  659.9 kB  1367  October 13, 2012 
Solid figures – Pyramid – easy  455.6 kB  1174  October 13, 2012 
Solid figures – Pyramid – medium  455.7 kB  1452  October 13, 2012 
Solid figures – Pyramid – hard  730.4 kB  928  October 13, 2012 
Solid figures – Pyramid – very hard  761.4 kB  867  October 13, 2012 
Cylinder


Solid figures – Cylinder – easy  455.2 kB  1541  October 13, 2012 
Solid figures – Cylinder – medium  455.2 kB  1541  October 13, 2012 
Solid figures – Cylinder – hard  640.2 kB  1082  October 13, 2012 
Solid figures – Cylinder – very hard  636.7 kB  948  October 13, 2012 
Cones


Solid figures – Cones – easy  455 kB  1508  October 13, 2012 
Solid figures – Cones – medium  455.1 kB  1226  October 13, 2012 
Solid figures – Cones – hard  639.1 kB  1047  October 13, 2012 
Solid figures – Cones – very hard  628.5 kB  853  October 13, 2012 
Spheres


Solid figures – Spheres – easy  455 kB  1298  October 13, 2012 
Solid figures – Spheres – medium  455 kB  1249  October 13, 2012 
Solid figures – Spheres – hard  634.2 kB  1041  October 13, 2012 
Solid figures – Spheres – very hard  637.9 kB  905  October 13, 2012 
Complete


Solid figures – Complete – very easy  647.7 kB  1802  October 13, 2012 
Solid figures – Complete – easy  456.1 kB  1718  October 13, 2012 
Solid figures – Complete – medium  456.1 kB  1981  October 13, 2012 
Solid figures – Complete – hard  681.9 kB  1180  October 13, 2012 
Solid figures – Complete – very hard  673.7 kB  1210  October 13, 2012 
Solid figures worksheets for students
Worksheet Name  File Size  Downloads  Upload date 
Identify each prism, pyramid, cylinder, cone or sphere  8.6 MB  2772  October 14, 2012 
Find the volume of each prism, pyramid, cylinder, cone or sphere  11.5 MB  2832  October 14, 2012 
Find the surface area of each prism, pyramid, cylinder, cone or sphere  11.8 MB  2106  October 14, 2012 