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?
Answer & explanation
Correct answer: option 3
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