The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the cylinder ?
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
Given: CSA of cylinder = 176 cm², Volume = 1232 cm³
CSA = $2\pi r h = 176$ ... (i)
Volume = $\pi r^2 h = 1232$ ... (ii)
Dividing (ii) by (i):
$$\frac{\pi r^2 h}{2\pi r h} = \frac{1232}{176}$$
$$\frac{r}{2} = 7 \implies r = 14 \text{ cm}$$
Substituting in (i):
$$2 \times \frac{22}{7} \times 14 \times h = 176$$
$$88h = 176 \implies h = 2 \text{ cm}$$
The height of the cylinder is 2 cm.
---
Explanation
- This question tests your ability to use two formulas simultaneously: CSA = $2\pi rh$ and Volume = $\pi r^2 h$.
- The key step is dividing Volume by CSA to eliminate $h$ and find $r$ first, then back-substitute to get $h$.
- Show both steps clearly for full marks — examiners award 1 mark for finding $r$ and 1 mark for finding $h$.