Correct Answer - Option 2 : 40 ∶ 1
Given:
Ratio of heights of the two right circular cylinders = 5 ∶ 2
The ratio of diameters of the two right circular cylinders = 4 ∶ 1
Formula Used:
The volume of the Cylinder = πr2h
where,
r = Radius of the cylinder
h = Height of the cylinder
Calculation:
Let the heights of the two right circular cylinders be 5x and 2x respectively
Let the radii of the two right circular cylinders be 2y and y/2 respectively. (Since Ratio of radii of two cylinders = ratio of diameters of the two cylinders)
Now, the ratio of the volumes of the two cylinders
⇒ (Volume of the first cylinder)/(Volume of the second cylinder)
⇒ [π × (2y)2 × 5x]/[π × y2/4 × 2x]
⇒ [π × 4y2 × 5x]/[π × y2/4 × 2x]
⇒ [40xy2]/[xy2]
⇒ 40/1
⇒ 40/1
⇒ 40 ∶ 1
∴ The ratio of the volumes of the two cylinders is 40 ∶ 1.