The slant height l can be found by using Pythagoras theorem. To find the total surface area of the cone, we need slant height of the cone, instead the perpendicular height. The lateral surface area of cone is given by:Įxample 7: Find the total surface area of a cone, whose base radius is 3 cm and the perpendicular height is 4 cm. So, the lateral surface area of the cone = 189.03 squared yard.Įxample 6: A circular cone is 15 inches high and the radius of the base is 20 inches What is the lateral surface area of the cone? Find the lateral surface area of the given cone. Find the curved surface area of cone.Įxample 5: Height and radius of the cone is 5 yard and 7 yard. So the base radius of the cone is 5 inch.Īnd the base diameter of the cone = 2 × radius = 2 × 5 = 10 inch.Įxample 3: What is the total surface area of a cone if its radius = 4cm and height = 3 cm.Īs mentioned earlier the formula for the surface area of a cone is given by:Īs in the previous example the slant can be determined using Pythagoras:Įxample 4: The slant height of a cone is 20cm. The total surface area of a cone = πrl + πr 2 = 375 inch 2 Step 3: Add all the areas together for the total surface area of a square prism, while the area of 6 rectangular faces gives the lateral area of the square prism. Step 2: Find the area of the six rectangular faces. If its slant height is four times the radius, then what is the base diameter of the cone? Use π = 3. Step 1: Calculate the area of the hexagonal base using the formula, 33a 2. Therefore, the total surface area of the cone is 83.17cm 2Įxample 2: The total surface area of a cone is 375 square inches. To begin with we need to find slant height of the cone, which is determined by using Pythagoras, since the cross section is a right triangle.Īnd the total surface area of the cone is: Add together the results of step one and step three. (more about conic section here )Įxample 1: A cone has a radius of 3cm and height of 5cm, find total surface area of the cone. Surface Area Formulas Rectangular Prism Multiply the perimeter of the base by the prisms height. The area of the curved (lateral) surface of a cone = πrlĪ cone does not have uniform (or congruent) cross-sections. So the surface area of the cone equals the area of the circle plus the area of the cone and the final formula is given by: The formula for the area of a cone is 3.14 times the radius times the side ( πrl ). Our base is side length a and for this calculation our height for the triangle is slant height s. You can now use the measurement of the side to find the area of the cone. Lateral Surface Area of a square pyramid (× 4 isosceles triangles) For the isosceles triangle Area (1/2)Base x Height. Make sure you use the same form of measurement as the radius. In order to do this, you must measure the side (slant height) of the cone. Now, you will need to find the area of the cone itself. The area of a circle is 3.14 times the radius squared ( πr 2 ). The next step is to find the area of the circle, or base. The first step in finding the surface area of a cone is to measure the radius of the circle part of the cone.
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