Mathematics — CBSE Class 10 board question

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.

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• 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 $h$.