How Do You Find the Surface Area of Cone with Slant Height and Diameter? In terms of height, the curved surface area of a right circular cone is given as πr(√(h 2 + r 2)) where "h" is the height of the right circular cone. Thus, the curved surface area of a right circular cone is given as πrl where "r" is the radius of the base and "l" is the slant height. What is the Curved Surface Area of a Right Circular Cone?Ī right circular cone is defined as the cone whose axis is the line joining the vertex and the midpoint of the circular base. In this, we do not consider the area of the base of the cone which is in the shape of a circle.
The formula to calculate the curved surface area of a cone is πrl where "r" is the radius of the base and "l" is the slant height of the cone.
The area of the curved surface of a cone is known as the curved surface area of the cone. Step 3: Simplify and write the answer in square units.If the total surface area of the cone has to be found, use the formula πr (r + l) square units, and if the curved surface area of the cone has to be found, use the formula πrl square units. Step 2: Use the appropriate formula to calculate the surface area.Step 1: Identify the given values of radius, slant height, and height of the cone.The surface area of a cone can be found by using the following steps: There are two types of the surface area of the cone that can be categorized as the total surface area and the curved surface area of the cone. The measure of the area occupied by the surface of a cone is referred to as the surface area of the cone. Let us look at some more examples of the surface area of a cone for a deeper understanding.įAQs on Surface Area of Cone What is the Surface Area of a Cone? ∴ The curved surface area of the cone is 66 in 2. The curved surface area of the cone, S = πrl = (22/7) × 7 × 3 = 66 in 2. ∴ The total surface area of the cone is 220 in 2. Given that: r = 7 inches, l = 3 inches, and π = 22/7. We know, the total surface area of the cone is πr (r + l), and the lateral surface area of a cone is πrl. Let us solve an example below to understand the application of the total surface area of cone and the curved surface area of cone.Įxample: Find the total surface area and curved surface area of the cone whose radius is 7 inches and slant height is 3 inches. ∴ The total surface area of cone, T = πr (r + l) units 2 Finding Surface Area of Cone ⇒ Total surface area of cone = πr 2 + πrl = πr (r + l). The total surface area of cone = area of the base of cone + curved surface area of a cone In order to determine the surface area of cone derivation, we cut the cone open from the center which looks like a sector of a circle (a plane shape). Let us take a cone of height "h", base radius "r", and slant height "l".
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