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 heights of A and B?
1. 16 : 3
2. 16 : 1
3. 1 : 16
4. 3 : 16
1. 16 : 3
2. 16 : 1
3. 1 : 16
4. 3 : 16
Correct Answer – Option 2 : 16 : 1
Given:
The capacity of cylinders A and B are equal.
Volume(A) = Volume(B)
The ratio of diameters = A ∶ B = 1 ∶ 4
Formula Used:
Volume of cylinder = πr2 h
Diameter = 2 × r
Where,
r → Radius of the cylinder
h → Height of the cylinder
Calculation:
r = D/2
The ratio of the radius of A and B
\(\Rightarrow \frac{{Diamater\;of\;A}}{{Diameter\;of\;B}} = 1/4\)
The capacity of cylinders A and B are equal.
Volume(A) = Volume(B)
⇒ π× r(A)2× h(A) = π× r(B)2× h(B)
⇒ r(A)2× h(A) = r(B)2× h(B)
⇒ r(A)2/r(B)2 = h(B)/ h(A)
⇒12/42 = h(B)/ h(A)
⇒1/16 = h(B)/ h(A)
⇒ h(A)/h(B) = 16/1
⇒ h(A) : h(B) = 16 : 1
∴ The ratio of the heights of A and B is 16 ∶ 1.