Let A and B be two cylinders such that the capacity of A is the same as the capacity of B. The ratio of the diameters of A and B is 1 : 4, what is the ratio of the height of A and B ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 16 : 1.
We know that,
Volume of cylinder = πr2h
Diameter = 2r
here, r = Radius of cylinder and H = Height
Now,
⇒ r = D/2
The ratio of the radius of A and B
Diameter of A/Diameter of B = 1/4
The volume(capacity) of the cylinder is equal
VolumeA = VolumeB
⇒ π × rA2 × hA = π × rB2 × hB
⇒ rA2 × hA = rB2 × hB
⇒ rA2/rB2 = hB/hA
⇒ 12/42 = hB/hA
⇒ 1/16 = hB/hA
⇒ hA/hB = 16/1
⇒ hA : hB = 16 : 1
The ratio of the heights of A and B = 16 : 1