In designing pistons, two cylinders have equal heights but one has twice the diameter of the other. What is the ratio of their volumes?
Show answer & explanation
Correct answer: B
Explanation
Given:
Two cylinders have the same height.
The diameter of one cylinder = 2 × the diameter of the other.
By the formula:
Volume of cylinder = πr²h
Diameter d ⇒ Radius r = d/2
Let the radius of the smaller cylinder = r
Radius of the larger cylinder = 2r
Height = h (same)
Volume ratio (smaller : larger)
= πr²h : π(2r)²h
= r² : 4r²
= 1 : 4