The radius of base and curved surface area of a right cylinder is '$r$' units and $4\pi rh$ square units respectively. The height of the cylinder is

### Concept & Logic The standard formula for the Curved Surface Area (CSA) of a cylinder relates its base radius and its actual height. $$ \text{CSA} = 2\pi \times \text{radius} \times \text{actual height} $$ ### Step-by-Step Solution 1. **Given:** - Radius of the base $= r$ - Curved Surface Area $= 4\pi rh$ 2. **Setup the Equation:** - Let the actual height of the cylinder be $H$. - According to the formula, $\text{CSA} = 2\pi rH$. 3. **Equate and Solve:** - $2\pi rH = 4\pi rh$ - Dividing both sides by $2\pi r$ (since radius $r$ is non-zero): - $H = 2h$ 4. **Conclusion:** - The height of the cylinder is $2h\text{ units}$. ### Exam Strategy & Shortcut By directly comparing the given expression $4\pi rh$ with the standard formula $2\pi rH$, you can mentally spot that the coefficient $4$ must be split into $2 \times 2$, meaning the height variable $H$ takes on the value $2h$. ### Common Pitfall Students might mistakenly assume the $h$ in the expression $4\pi rh$ represents the actual height of the cylinder and blindly select option (b) without working through the equivalence. ### Final Answer Therefore, the correct answer is **$2h\text{ units}$**.