A solid cone has a lateral surface area of $100\pi$ square centimeters and a total surface area of $269\pi$ square centimeters. Find the base radius of the cone.
I would need to find the radius or height to solve this, but all it gives me is the lateral surface area of $100\pi$ and the total surface area of $269\pi$.
Both formulas require the height and the radius and it doesn't give me either. It wants me to find the base radius of the cone, the formula for that is $AB=\pi r^2$. I tried putting $269\pi$ (the number of the total surface area) in the formula: $269\pi= πr^2$, Which is $844.66= 3.14 r^2$ which would mean the radius is $9.9$. I tried putting in with the two formulas for the lateral surface area and total surface area, but they both don't work right with that number.