Check the picture below.
so, bearing in mind that, the radius and height are two sides in a right-triangle, thus both are at a ratio of each other, thus the radius is at 3:4 ratio in relation to the height.
![\bf 12\pi =\cfrac{\pi \cdot 3^2h^2 h}{4^2}\implies 12\pi =\cfrac{9\pi h^3}{16}\implies \cfrac{192\pi }{9\pi }=h^3 \\\\\\ \sqrt[3]{\cfrac{192\pi }{9\pi }}=h\implies \sqrt[3]{\cfrac{64}{3}}=h\implies \cfrac{4}{\sqrt[3]{3}}=h \\\\\\ \cfrac{4}{\sqrt[3]{3}}\cdot \cfrac{\sqrt[3]{3^2}}{\sqrt[3]{3^2}}=h\implies \cfrac{4\sqrt[3]{9}}{\sqrt[3]{3^3}}=h\implies \cfrac{4\sqrt[3]{9}}{3}=h](https://tex.z-dn.net/?f=%5Cbf%2012%5Cpi%20%3D%5Ccfrac%7B%5Cpi%20%5Ccdot%203%5E2h%5E2%20h%7D%7B4%5E2%7D%5Cimplies%2012%5Cpi%20%3D%5Ccfrac%7B9%5Cpi%20h%5E3%7D%7B16%7D%5Cimplies%20%5Ccfrac%7B192%5Cpi%20%7D%7B9%5Cpi%20%7D%3Dh%5E3%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7B%5Ccfrac%7B192%5Cpi%20%7D%7B9%5Cpi%20%7D%7D%3Dh%5Cimplies%20%5Csqrt%5B3%5D%7B%5Ccfrac%7B64%7D%7B3%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%7D%7B%5Csqrt%5B3%5D%7B3%7D%7D%3Dh%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B4%7D%7B%5Csqrt%5B3%5D%7B3%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%5Csqrt%5B3%5D%7B9%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E3%7D%7D%3Dh%5Cimplies%20%5Ccfrac%7B4%5Csqrt%5B3%5D%7B9%7D%7D%7B3%7D%3Dh)
so, bearing in mind that, the radius and height are two sides in a right-triangle, thus both are at a ratio of each other, thus the radius is at 3:4 ratio in relation to the height.