Solid figures

Solid figures are objects in three-dimensional 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.

solid figures

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 three-dimensional 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 two-dimensional 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 * r3

The surface area of a sphere (A ) is calculated in a similar way, using this formula:

A = 4 * π * r2

 

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 * r2

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 three-dimensional  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 1991 October 13, 2012
Solid figures – Prism – easy 455.8 kB 1453 October 13, 2012
Solid figures – Prism – medium 456.2 kB 1610 October 13, 2012
Solid figures – Prism – hard 716.1 kB 951 October 13, 2012
Solid figures – Prism – very hard 702.6 kB 874 October 13, 2012
Pyramid
Solid figures – Pyramid – very easy 659.9 kB 1114 October 13, 2012
Solid figures – Pyramid – easy 455.6 kB 903 October 13, 2012
Solid figures – Pyramid – medium 455.7 kB 991 October 13, 2012
Solid figures – Pyramid – hard 730.4 kB 652 October 13, 2012
Solid figures – Pyramid – very hard 761.4 kB 612 October 13, 2012
Cylinder
Solid figures – Cylinder – easy 455.2 kB 1204 October 13, 2012
Solid figures – Cylinder – medium 455.2 kB 1031 October 13, 2012
Solid figures – Cylinder – hard 640.2 kB 808 October 13, 2012
Solid figures – Cylinder – very hard 636.7 kB 689 October 13, 2012
Cones
Solid figures – Cones – easy 455 kB 1150 October 13, 2012
Solid figures – Cones – medium 455.1 kB 927 October 13, 2012
Solid figures – Cones – hard 639.1 kB 797 October 13, 2012
Solid figures – Cones – very hard 628.5 kB 622 October 13, 2012
Spheres
Solid figures – Spheres – easy 455 kB 1034 October 13, 2012
Solid figures – Spheres – medium 455 kB 925 October 13, 2012
Solid figures – Spheres – hard 634.2 kB 787 October 13, 2012
Solid figures – Spheres – very hard 637.9 kB 650 October 13, 2012
Complete
Solid figures – Complete – very easy 647.7 kB 1373 October 13, 2012
Solid figures – Complete – easy 456.1 kB 1277 October 13, 2012
Solid figures – Complete – medium 456.1 kB 1524 October 13, 2012
Solid figures – Complete – hard 681.9 kB 861 October 13, 2012
Solid figures – Complete – very hard 673.7 kB 885 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 2287 October 14, 2012
Find the volume of each prism, pyramid, cylinder, cone or sphere 11.5 MB 2184 October 14, 2012
Find the surface area of each prism, pyramid, cylinder, cone or sphere 11.8 MB 1627 October 14, 2012