Question
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
When the length height is 22cm and the diameter is 25 cm
Answers
Answered by
GPT 3.5
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).
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).
There are no human answers yet. A form for humans to post answers is coming very soon!