For a closed cylindrical container, the radius and the height add up to 37 cm, and the total surface area is 3,256 cm². What is its volume? Take $\pi = \frac{22}{7}$.

Explanation

1. 01

   Total surface = $2\pi r (r + h) = 2 \times \frac{22}{7} \times r \times 37$.

2. 02

   So $\frac{1628}{7} r = 3256$, giving $r = 14$ cm and $h = 37 - 14 = 23$ cm.

3. 03

   Volume = $\frac{22}{7} \times 14 \times 14 \times 23 = 14{,}168$ cm³.