Use the image to answer the question.
A cone shows a base diameter of 25 centimeters, perpendicular height from the base to the top vertex at 90 degrees, and 22 centimeters as the hypotenuse or the side of the cone.
What is the surface area of the cone? Use 3.14 for pi.
To find the surface area of the cone, we need to calculate the lateral surface area and the base area separately, and then add them together.
The lateral surface area of a cone can be calculated using the formula:
Lateral surface area = π * r * l
where r is the radius of the base and l is the slant height (also known as the side of the cone).
In the given image, we are given the diameter of the base, which is 25 centimeters. The radius (r) can be calculated by dividing the diameter by 2:
r = 25 cm / 2 = 12.5 cm
The slant height (l) is given as 22 centimeters.
Now, we can calculate the lateral surface area:
Lateral surface area = π * r * l
Lateral surface area = 3.14 * 12.5 cm * 22 cm
Lateral surface area ≈ 3.14 * 275 cm^2
Lateral surface area ≈ 863.5 cm^2
Next, we need to calculate the base area of the cone. The base of a cone is a circle, and the area of a circle can be calculated using the formula:
Base area = π * r^2
Using the previously calculated radius (r = 12.5 cm), we can calculate the base area:
Base area = π * r^2
Base area = 3.14 * (12.5 cm)^2
Base area ≈ 3.14 * 156.25 cm^2
Base area ≈ 490.625 cm^2
Finally, we can calculate the total surface area by adding the lateral surface area and the base area:
Total surface area = Lateral surface area + Base area
Total surface area ≈ 863.5 cm^2 + 490.625 cm^2
Total surface area ≈ 1354.125 cm^2
Therefore, the surface area of the given cone is approximately 1354.125 square centimeters.