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  2252  October 13, 2012 
Solid figures – Prism – easy  455.8 kB  1746  October 13, 2012 
Solid figures – Prism – medium  456.2 kB  1889  October 13, 2012 
Solid figures – Prism – hard  716.1 kB  1142  October 13, 2012 
Solid figures – Prism – very hard  702.6 kB  1042  October 13, 2012 
Pyramid


Solid figures – Pyramid – very easy  659.9 kB  1254  October 13, 2012 
Solid figures – Pyramid – easy  455.6 kB  1066  October 13, 2012 
Solid figures – Pyramid – medium  455.7 kB  1228  October 13, 2012 
Solid figures – Pyramid – hard  730.4 kB  815  October 13, 2012 
Solid figures – Pyramid – very hard  761.4 kB  761  October 13, 2012 
Cylinder


Solid figures – Cylinder – easy  455.2 kB  1383  October 13, 2012 
Solid figures – Cylinder – medium  455.2 kB  1271  October 13, 2012 
Solid figures – Cylinder – hard  640.2 kB  959  October 13, 2012 
Solid figures – Cylinder – very hard  636.7 kB  836  October 13, 2012 
Cones


Solid figures – Cones – easy  455 kB  1351  October 13, 2012 
Solid figures – Cones – medium  455.1 kB  1097  October 13, 2012 
Solid figures – Cones – hard  639.1 kB  950  October 13, 2012 
Solid figures – Cones – very hard  628.5 kB  752  October 13, 2012 
Spheres


Solid figures – Spheres – easy  455 kB  1187  October 13, 2012 
Solid figures – Spheres – medium  455 kB  1119  October 13, 2012 
Solid figures – Spheres – hard  634.2 kB  929  October 13, 2012 
Solid figures – Spheres – very hard  637.9 kB  786  October 13, 2012 
Complete


Solid figures – Complete – very easy  647.7 kB  1596  October 13, 2012 
Solid figures – Complete – easy  456.1 kB  1546  October 13, 2012 
Solid figures – Complete – medium  456.1 kB  1804  October 13, 2012 
Solid figures – Complete – hard  681.9 kB  1049  October 13, 2012 
Solid figures – Complete – very hard  673.7 kB  1075  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  2536  October 14, 2012 
Find the volume of each prism, pyramid, cylinder, cone or sphere  11.5 MB  2559  October 14, 2012 
Find the surface area of each prism, pyramid, cylinder, cone or sphere  11.8 MB  1887  October 14, 2012 