A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder. If their radii are in the ratio 3 : 1, then the volume of the smaller cylinder is approximately _____% of the larger cylinder (the smaller cylinder has its radius and height smaller when compared to the larger).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9.52.
Volume of cylinder = πr2h
Curved surface area of cylinder = 2πrh
Where r is the radius and h is the height of the cylinder
Let the radius of the larger cylinder and smaller cylinder be 3x and x.
The height of the larger cylinder and smaller cylinder is h1 and h2.
So, 2π(3x)h1 = (350/100)2π(x)h2
⇒ h1/h2 = 3.5/3 = 7/6
Volume of larger cylinder = π(3x)2 × 7 = 63πx2
Volume of smaller cylinder = π(x)² × 6 = 6πx2
Required percentage = (6πx2/63πx2) × 100 = 9.523...% = 9.52% (approx)
Therefore, the volume of the smaller cylinder is 9.52% of the larger cylinder.