The height of a cylinder is (2/3)rd of its diameter. Its volume is equal to the volume of a sphere whose radius is 4 cm. What is the curved surface area (in cm2) of the cylinder?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. (128/3)π
Let r cm be the radius and h cm height of the cylinder. Then,
h = (2/3) diameter = 2/3 × 2r = 4r/3
Now,
The volume of the cylinder = Volume of the sphere of radius 4 cm
πr2h = 4/3 × π × 4 × 4 × 4
⇒ πr2 × 4r/3 = 4/3 × π × 4 × 4 × 4
⇒ r = 4
⇒ h = 16/3
Curved surface area (in cm2) of the cylinder :
2πrh = (2 × 4 × 16/3)π = (128/3)π