If a cone has a Surface Area of 417π and a diameter of 6 determine its slant height.
SA= πrs+πr^2
417π= π3s+π3^2
1310.0044137=π3s+π3^2
Divide by π
417 divide by π
132.7352225= 3s+3^2
Now I don't know what to do
SA=πrs+πr^2
417π=π3S+π3^2
417π= π(3S+9
(417π)/π = [π(3s+9)]/π
417= 3s+9
417-9= 3s+9-9
408=3s
408/3=3s/3
136=S
To determine the slant height of the cone, we can use the formula for the surface area of a cone:
Surface Area = πr(r + l)
where r is the radius of the base and l is the slant height.
Given that the diameter of the cone is 6, we can find the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 6 / 2 = 3
Now, we can substitute the values into the formula:
417π = π(3)(3 + l)
To solve for l, we divide both sides of the equation by π(3):
417π / (π(3)) = 3 + l
Cancelling out the π's:
417 / (3) = 3 + l
139 = 3 + l
To solve for l, we subtract 3 from both sides of the equation:
139 - 3 = 3 + l - 3
136 = l
Therefore, the slant height of the cone is 136.