![]() The latter equation shows that the total surface area includes the lateral area π x r x √(r² + h²) and the area of the cone's circular base π x r²:Ī_T = Total area = Lateral area + base areaįrom here we can see that if the total and base areas of a cone are known, we could also determine its lateral surface area as the difference between these:Ī_L = Lateral area = Total area - base areaĪnother option to calculate the lateral area of a cone is from its volume and radius or volume and vertical height. For the particular case of a cone, we'll only be excluding the base since this figure does not have a top. ![]() Volume of a Prism The volume V of a right prism is given by the formula V B h, where B is the area of the base and h is the height. This is, the sides of the shape, excluding its base and top. (The cube is a special case.) Similarly, a prism with a 5 -sided base is a pentagonal prism, a prism with a 6 -sided base is a hexagonal prism, etc. Regular hexagonal prism (1) volume: V 3 23a2h (2) surface area: S 33a2+6ah R e g u l a r h e x a g o n a l p r i s m ( 1) v o l u m e: V 3 2 3 a 2 h ( 2) s u r f a c e a r e a: S 3 3 a 2 + 6 a h. Here is how the Lateral Surface Area of Hexagonal Prism calculation can be. From the equation above, you might have noticed that the lateral surface area of a cone does not correspond to its total surface area, given by:įor any geometrical figure, the difference between these two areas is that the lateral surface area of a three-dimensional shape is the area that can be seen from a side-on view. The surface area (or total surface area) of a hexagonal prism is the entire.
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