The sum of the radius of the base and the height of a solid circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm², find the volume of the cylinder. (Use \(\pi = \frac{22}{7}\))

4615 cm³
4610 cm³
4620 cm³
2620 cm³

Correct answer: 4620 cm³

Solution

For a cylinder, TSA = 2\pi r(r+h). Given r+h = 37 and TSA = 1628, we get 2\pi r \cdot 37 = 1628. Using \(\pi = 22/7\), this gives \(r = 7\) and \(h = 30\), so volume = \(\pi r^2 h = \frac{22}{7}\times 49 \times 30 = 4620\) cm³.

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