Formula for surface area of a cone: S=πrl + πr^2. Solve for l. Then find l when S=283cm^2 and r =5cm.

Hello!
Here r is the radius of a (right circular) cone. S = pi r^2 is the area of its base, and l is its slant height.
To solve the equation S = pi r l + pi r^2 for l (when we know S and r ), we move pi r^2 to the left: S - pi r^2 = pi r l, and then we divide both sides by pi r. This way we finally obtain
l = (S - pi r^2)/(pi r) = S/(pi r) - r.
It is the formula we want (any of the two versions).

Now we can use this formula for the given S = 283 cm^2 and r = 5 cm:
l = 283/(pi * 5) - 5 approx 283/(3.14 * 5) - 5 approx 13 (cm).
So the slant height l of the cone must be approximately 13 cm.