Question
What is the surface area of the cone if the slant height is 22 cm and the diameter equals 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 to the lateral surface area.
The diameter of the cone is given as 25 cm, which means that the radius is half of that, or 25/2 = 12.5 cm.
The slant height of the cone is given as 22 cm.
The lateral surface area of the cone can be calculated using the formula: Lateral surface area = π * radius * slant height.
Lateral surface area = π * 12.5 cm * 22 cm = 275π cm².
The formula to find the area of the base of the cone is: Base area = π * radius².
Base area = π * (12.5 cm)² = 156.25π cm².
Therefore, the surface area of the cone is the sum of the lateral surface area and the base area:
Surface area = Lateral surface area + Base area
Surface area = 275π cm² + 156.25π cm²
Surface area = 431.25π cm².
To find an approximate value, you can use a calculator and multiply 431.25 by π, or you can leave the answer in terms of π.
The diameter of the cone is given as 25 cm, which means that the radius is half of that, or 25/2 = 12.5 cm.
The slant height of the cone is given as 22 cm.
The lateral surface area of the cone can be calculated using the formula: Lateral surface area = π * radius * slant height.
Lateral surface area = π * 12.5 cm * 22 cm = 275π cm².
The formula to find the area of the base of the cone is: Base area = π * radius².
Base area = π * (12.5 cm)² = 156.25π cm².
Therefore, the surface area of the cone is the sum of the lateral surface area and the base area:
Surface area = Lateral surface area + Base area
Surface area = 275π cm² + 156.25π cm²
Surface area = 431.25π cm².
To find an approximate value, you can use a calculator and multiply 431.25 by π, or you can leave the answer in terms of π.