Surface Area of Solids

Surface Area of Prisms

The surface area of a prism can be easily calculated using its net.
The net of a prism consists of two congruent bases and rectangular lateral faces, as shown in the diagram. Therefore, the surface area of a prism is the sum of the areas of the two bases and the lateral faces.
Similarly, the net of a cylinder consists of two congruent circles and a rectangular lateral face. Thus, the surface area of a cylinder can also be calculated by adding the areas of the two bases and the lateral face.

Surface Area of a Prism


For a cylinder with a base radius and height , the net consists of two circular bases and a rectangular lateral face. Therefore, its surface area is given by:

Surface Area of Pyramids

Like prisms, the surface area of a pyramid can also be calculated using its net.
The net of a pyramid consists of a single base and several triangular lateral faces, as shown in the diagram.
Hence, the surface area of a pyramid is the sum of the base area and the lateral area.

The net of a cone consists of a circular base and a sector-shaped lateral face. The surface area of a cone is also the sum of the areas of its base and lateral face.

Surface Area of a Pyramid

For a cone with a base radius and slant height , the base is a circle and the lateral face is a sector. Their areas are:
Thus, the surface area of a cone is given by:

Surface Area of Spheres

The surface area of a sphere with radius is known to be four times the area of a circle with the same radius. Therefore, the surface area of a sphere can be calculated as follows:

Surface Area of a Sphere

For a sphere with radius , the surface area is: