What is the surface area of the cone? Use 3.14 for pi. The slant height is 22 cm and the length is 25 cm.
To determine the surface area of a cone, we need to calculate the area of the base and the lateral surface area.
First, let's calculate the radius of the cone's base:
radius = length / 2 = 25 cm / 2 = 12.5 cm
Now, let's calculate the area of the base:
base area = π * radius^2 = π * (12.5 cm)^2 = 3.14 * 156.25 cm^2 = 490.875 cm^2
Next, let's calculate the lateral surface area using the slant height (l) and the radius (r):
lateral surface area = π * r * l
lateral surface area = 3.14 * 12.5 cm * 22 cm = 868.5 cm^2
Finally, we can calculate the total surface area by summing the base area and the lateral surface area:
surface area = base area + lateral surface area = 490.875 cm^2 + 868.5 cm^2 = 1359.375 cm^2
Therefore, the surface area of the cone is 1359.375 cm^2.