Pyramid and Cone
Pyramid
Lateral Area of a Regular Pyramid: If a regular pyramid has a lateral area of L square units, a base with a perimeter of P units, and a slant height of units, then L = ¹⁄2 Pl
Surface Area of a Regular Pyramid: If a regular pyramid has a surface area of S square units, a slant height of units, and a base with perimeter of P units and area of B square units, then S = ¹⁄2 Pl + B
Volume of a Pyramid: If a pyramid has a volume of V cubic units and a height of h units and the area of the base is B square units, then V = ¹⁄3 Bh
Cone
The slant height of a cone is the length of any segment whose endpoints are the vertex of the cone and a point on the circle that forms the base.
The formulas for finding the lateral area and surface area of a cone are similar to those for a regular pyramid. However, since the base is a circle, the perimeter becomes the circumference, and the area of the base is π r² square units.
Read the explanation below to know more about pyramids and cones.
Practice: Find the volumes of prisms, cylinders, pyramids and cones in the following exercises.