Step-by-step explanation:
[tex]CSA\: of \:cylinder = 2πrh\\TSA\: of\:cylinder = 2πr(r+h)\\By \: conditions,\\2πrh =\frac{2}{3}\times2πr(r+h)\\3h = 2\times(r+h)\\3h = 2r + 2h\\h = 2r\\Also,\\2πr(r+h) = 924\\2\times\frac{22}{7}\times r(r+2r) = 924\\ \frac{44}{7} \times r(3r) = 924 \\ 3r^{2} = 924 \times \frac{7}{44} \\ 3r² = 147\\r²=\frac{147}{3}\\r² = 49\\r=\sqrt{47}\\ r = 7\\h = 2 \times 7 = 14\\hence\:radius=7cm,\:height=14cm\\[/tex]
