The volume of a cylinder with a base radius of 3 cm is 396 cm³. Find its curved surface area (in cm²).

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Accepted Answer

1. **Use the formula for the volume of a cylinder:**  
   - Volume $$V = \pi r^2 h$$, where $$r$$ is the radius and $$h$$ is the height.  
   - Substituting the given values:  
     $$
     396 = \pi (3)^2 h.
     $$  
   - Simplify:  
     $$
     396 = \pi 	imes 9 	imes h \implies h = \frac{396}{9\pi}.
     $$  
   - Approximate $$\pi$$ as 3.14:  
     $$
     h = \frac{396}{28.26} \approx 14 \, 	ext{cm}.
     $$

2. **Calculate the curved surface area (CSA):**  
   - CSA formula: $$2\pi r h$$.  
   - Substituting values:  
     $$
     CSA = 2 	imes 3.14 	imes 3 	imes 14.
     $$  
   - Simplify:  
     $$
     CSA = 264 \, 	ext{cm}^2.
     $$

Thus, the curved surface area of the cylinder is **264 cm²**.

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