Question

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the diameter and the height of the pillar.

Answer 1

Here, r  m= radius of the cylinder
         h m= height of the cylinder

Curved surface area of the cylinder = 2πrh     ... (1)
Volume of the cylinder = πr²h                        ... (2)
            924 = πr²h

\[h = \frac{924}{\pi r^2}\]
Then, substitute h into equation (1):
264 = 2πrh
\[264 = 2\pi r\left( \frac{924}{\pi r^2} \right)\]
264r = 2(924)

\[r = \frac{2 \times 924}{264}\]

r = 7 m, so d = 14 m

\[h = \frac{924}{\pi r^2}\]
h = \[\frac{924}{\frac{22}{7} \times 7^2} = 6 m\]

Hence, the diameter and the height of the cylinder are 14 m and 6 m, respectively.