We can do this with a simple triple integral and some algebra.
If you split the cylinder into very small circular slices, each of those slices would have a volume equal to (Area of Circle)*(Δh). To find the area of each circular slice, we can take the circle to be a series of concentric disks, each with a width Δr. Using polar coordinates, we can express the area of the circle as a double integral. Since each disk goes about a 360 degree rotation (or 2π) this will be our angle of integration, giving us the following integral: ∫(0-2π)∫(0-R)[rdrdθ]
We now take this integral, and integrate it over our height of 10cm, and this integral will be equal to the volume of the cylinder, which is 300cm^3
So our equation is:
300 = ∫(0-10) ∫(0-2π)∫(0-R)[rdrdθdh]
300 =10 (∫(0-2π)∫(0-R)[rdrdθ])
30 = 2π(∫(0-R)[rdr])
30 = 2π[(r^2)/2](0-R)
30=π(r^2)
sqrt(30/π) = r
r ~ 3.1
Therefore the answer is A) 3.1cm