If the total surface area of a cylinder is 704 cm2 and the ratio of height to base radius of the cylinder is 3 : 4, then what will be the volume of that cylinder?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 384π cm3.
The height and base radius of the cylinder are 3x and 4x, respectively.
Total surface area of the cylinder = 2πr(h + r)
704 = 2 × (22/7) × 4x × (3x + 4x)
⇒ 704 = 176x/7 × (3x + 4x)
⇒ 704 = 176x2
⇒ x2 = 4
⇒ x = 2
Base radius = 4x = 8 cm
Height = 3x = 6 cm
Volume of the cylinder = πr2h = π × 64 × 6 = 384π cm3