The curved surface area of a right circular cylinder is 616 cm² and the area of its base is 38.5 cm². What is the volume (in cm³) of the cylinder? (Use π = \(\frac{22}{7}\)) 

Given:

The curved surface area of a right circular cylinder is 616 cm²

The area of its base is 38.5 cm²

Formula used:

Curved Surface Area (CSA) = 2πrh

Area of Base = πr²

Volume = πr²h

Calculation:

CSA = 616 cm²

⇒ 2πrh = 616

⇒ 2 × (22/7) × r × h = 616

⇒ rh = 616 × 7 / 44 = 98

Area of Base = 38.5 cm²

⇒ πr² = 38.5

⇒ (22/7) × r² = 38.5

⇒ r² = 12.25

⇒ r = √12.25 = 3.5 cm

Now, rh = 98

⇒ 3.5h = 98

⇒ h = 28 cm

Volume = πr²h

⇒ Volume = (22/7) × (3.5)² × 28

⇒ Volume = (22/7) × 12.25 × 28

⇒ Volume = 1078 cm³

∴ The correct answer is option 1.