The volume of a cylinder having base radius 3 cm is 396 cm3. Find its curved surface area (in cm2). (Use \(\pi =\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 264
The volume \(\pi r^{2}h\) gives the height, and the curved surface area is \(2\pi rh\): opened out, the curved surface is a rectangle as long as the base circle (\(2\pi r\)) and as high as the cylinder (h).
From the volume: \(\displaystyle \frac{22}{7}\times3\times3\times h=396\)
Height \(\displaystyle h=\frac{396\times7}{198}=14\,\mathrm{cm}\)
Curved surface area \(\displaystyle =2\times\frac{22}{7}\times3\times14=264\,\mathrm{cm^2}\)
Shortcut: Curved surface area and volume share \(\pi rh\), so the height need not be found.
\(\displaystyle \frac{2\pi rh}{\pi r^{2}h}=\frac{2}{r}\), so curved surface area \(\displaystyle =\frac{2V}{r}\)
With \(V=396\) and \(r=3\): \(\displaystyle \frac{2\times396}{3}=264\,\mathrm{cm^2}\)