The areas of the curved surface and the base of a right circular cylinder are ‘a’ sq.cm and b’ sq.cm respectively. The height of the cylinder (in cm) is :

Correct option is C

Given:
Curved Surface Area (CSA) of the cylinder = a sq. cm
Base Area (BA) of the cylinder = b sq. cm
Formulas:
Curved Surface Area (CSA) of a cylinder: CSA = 2πrh, where r is the radius and h is the height.
Base Area (BA) of a cylinder: BA = πr²
Step-by-step Solution:
From the formula for the base area:
πr² = b → r² = b/π → r = √(b/π)
Substitute the value of r into the formula for the curved surface area:
2πrh = a
Substituting r = √(b/π):
2π(√(b/π))h = a
Simplify the equation:
2π × (√(b/π)) × h = a
2π × (√b/√π) × h = a
2√π √b × h = a
h = a / (2√π √b)