To find the surface area of a cone, you need to add the area of the base and the lateral surface area.
The base of the cone is a circle, so its area is given by A_base = π * (r_base)^2, where r_base is the radius of the base.
Given that the diameter of the base is 25 cm, the radius is half of that, so r_base = 25 cm / 2 = 12.5 cm.
Therefore, A_base = 3.14 * (12.5 cm)^2 = 3.14 * 156.25 cm^2 ≈ 490.875 cm^2 (rounded to three decimal places).
The lateral surface area of the cone is given by A_lateral = π * r * l, where r is the radius of the base and l is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem: slant height^2 = height^2 + radius^2.
Given that the height is 22 cm and the radius is 12.5 cm, the slant height is slant height ≈ sqrt((22 cm)^2 + (12.5 cm)^2) ≈ 25.065 cm.
Therefore, A_lateral = 3.14 * 12.5 cm * 25.065 cm ≈ 985.425 cm^2 (rounded to three decimal places).
Adding the base area and the lateral surface area, the total surface area of the cone is approximately:
A_total = A_base + A_lateral ≈ 490.875 cm^2 + 985.425 cm^2 ≈ 1476.3 cm^2 (rounded to three decimal places).
What is the surface area of the cone? Use 3.14 for pi
When the length height is 22cm and the diameter is 25 cm
1 answer
1 answer