The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. The ratio of its diameter to its height is: (Use \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7 : 3
The curved surface area of a cylinder is \(2\pi rh\) and its volume \(\pi r^2h\). Dividing the volume by the curved surface area cancels \(\pi\) and \(h\) and leaves the radius alone.
Curved surface area: \(2\pi rh=264\) (1)
Volume: \(\pi r^2h=924\) (2)
Dividing (2) by (1), \(\pi\) and \(h\) cancel: \(\displaystyle \frac{r}{2}=\frac{924}{264}=3.5\), so \(r=7\) m
From (1): \(\displaystyle 2\times\frac{22}{7}\times7\times h=264\), so \(44h=264\) and \(h=6\) m
Diameter, twice the radius \(=2\times7=14\) m
Diameter : height \(=14:6=7:3\)