Question

The curved surface area and volume of a cylinder are 264 m\(^2\) and 396 m\(^3\) respectively. Find the radius and height of the cylinder.

Hint:

Divide volume by CSA to simplify the radius-height relationship.

Answer 1

Curved Surface Area (CSA) of a cylinder:
\[ 2\pi rh = 264. \] Volume of a cylinder:
\[ \pi r^2 h = 396. \] Dividing:
\[ \frac{2\pi rh}{\pi r^2 h} = \frac{264}{396}. \] \[ \frac{2}{r} = \frac{2}{3}. \] \[ r = 3. \] Substituting in \( 2\pi rh = 264 \):
\[ 2\pi (3)h = 264. \] \[ 6\pi h = 264. \] \[ h = \frac{264}{6\pi} = 14. \]