How do you find the slant height of a cone using the surface area and radius?
Surface Area = 275.7 m^2
Radius = 4.5m
To find the slant height of a cone using the surface area and radius, you can use the formula for the surface area of a cone and solve for the slant height.
The formula for the surface area of a cone is:
Surface Area = πr(r + l)
Given that the surface area is 275.7 m^2 and the radius is 4.5m, we can plug in these values to the formula:
275.7 = π(4.5)(4.5 + l)
Now, we can simplify and solve for l (the slant height):
275.7 = 20.25π + πl
255.45 = πl
l = 255.45 / π
l ≈ 81.26 m
Therefore, the slant height of the cone is approximately 81.26 meters.