1. **State the problem:** We have a cylinder with diameter 20 cm and curved surface area (CSA) 200 cm². We need to find its volume in cm³. 2. **Recall formulas:** - Diameter $d = 20$ cm, so radius $r = \frac{d}{2} = 10$ cm. - Curved surface area of a cylinder: $\text{CSA} = 2\pi r h$ where $h$ is the height. - Volume of a cylinder: $V = \pi r^2 h$. 3. **Find height $h$ using CSA:** $$200 = 2\pi \times 10 \times h$$ $$200 = 20\pi h$$ Divide both sides by $20\pi$: $$h = \frac{200}{20\pi} = \frac{200}{\cancel{20}\pi \cancel{}} = \frac{10}{\pi}$$ 4. **Calculate volume $V$:** $$V = \pi \times 10^2 \times \frac{10}{\pi} = \pi \times 100 \times \frac{10}{\pi}$$ Cancel $\pi$: $$V = \cancel{\pi} \times 100 \times \frac{10}{\cancel{\pi}} = 1000$$ 5. **Final answer:** The volume of the cylinder is $1000$ cm³. **Note:** None of the options exactly match $1000$. Please verify options or problem data.