The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm², then what is the volume (in cm³) of the cylinder?

4312 \(\frac{28}{\sqrt {6 }}\) cm³

CSA : TSA = 2 : 5

TSA =  5R = 3080  (given)

1R =616

CSA = 2R = 2 × 616 = 1232

TSA = CSA + 2\(\pi \)r²

3080 = 1232 + 2\(\pi \)r²

1848 = 2\(\pi \)r²

r² = 294

r = 7\(\sqrt {6 }\)  

CSA = 2\(\pi \)rh = 1232

2 × \(\frac{22}{7}\) × 7\(\sqrt {6 }\) × h = 1232

h = 1232 × \(\frac{7}{44}\) ×  \(\frac{1}{7\sqrt {6 }}\)

h = \(\frac{28}{\sqrt {6 }}\)

Volume = \(\pi \)r²h

= \(\pi \) (7 \(\sqrt {6}\))² x \(\frac{28}{\sqrt {6}}\)

= 4312\(\frac{28}{\sqrt {6 }}\) cm³