Surface Area of Cones and Pyramids

The total surface area of a cone is given by the formula: $$A = \frac{1}{2}Pl + \frac{1}{2}\times \text{Base Area}$$ , where P is the perimeter of the base and l is the slant height.

The total surface area of a pyramid is given by the formula: $$A = \frac{1}{2}Pl + B$$ , where P is the perimeter of the base, l is the slant height, and B is the area of the base.

The lateral surface area of a cone is calculated using the formula: $$A_{lateral} = \frac{1}{2}Pl$$ , where P is the perimeter of the base and l is the slant height.

The lateral surface area of a pyramid can be calculated using the formula: $$A_{lateral} = \frac{1}{2}Pl$$ , where P is the perimeter of the base and l is the slant height.

The base area of a cone is calculated using the formula: $$B = \text{Area} = \text{π}r^2$$ .

The base area of a pyramid with a square base is calculated using the formula: $$B = s^2$$ .

The slant height of a cone can be found using the Pythagorean theorem: $$l = \text{√}(r^2 + h^2)$$ , where r is the radius and h is the height of the cone.

The height of a pyramid can be found using the formula: $$h = \frac{3V}{B}$$ , where V is the volume and B is the base area.

To find the total surface area, first calculate the slant height: $$l = \text{√}(3^2 + 4^2) = 5 cm$$ . Then use the formula: $$A = \frac{1}{2} \times 2\text{π} \times 3 \times 5 + \text{π} \times 3^2 = 47.12 cm^2$$ .

First, calculate the base area: $$B = 4^2 = 16 cm^2$$ . Then find the slant height: $$l = \text{√}(4^2 + 6^2) = 7.21 cm$$ . Finally, use the formula: $$A = \frac{1}{2} \times 4 \times 7.21 + 16 = 29.84 cm^2$$ .