How Do You Find the Lateral and Surface Areas of a Cone?

1. The lateral area is the area of the curved surface of the cone
1. π, or pi, is an irrational number we can approximate as 3.14
2. The base of a cone is always a circle
3. The slant height is the measurement from the tip of the cone to any point on the edge of its base
4. 'r', the radius of the base, is 1.7 ft
5. 'l', the slant height, is 2 ft
6. So 'L', the lateral area, is (3.14)(1.7)(2), or 10.676 ft²
1. We need to find the area of the base before we can find the surface area
2. Remember, the base of a cone is always a circle
1. π, or pi, is an irrational number we can approximate as 3.14
2. The radius of our base was 1.7 ft
3. So B, the area of the base is (3.14)(1.7)², or 9.0746 ft²
1. The surface area is equal to the lateral area plus the area of the base
1. Our lateral area, L, was 10.676
2. The area of our base, B, was 9.0746
3. Adding these two numbers together, we get 19.7506 ft² as the surface area of our cone

Find the lateral and surface areas of the given cone