The curved surface area and the volume of a cylinder are 660 cm2 and 1650 cm3 respectively. What is the height of the cylinder? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21 cm
The volume of a cylinder is \(\pi r^2h\) and its curved surface area is \(2\pi rh\). Dividing the volume by the curved surface area cancels \(\pi\) and \(h\) and leaves \(\displaystyle \frac{r}{2}\), which gives the radius first.
\(\displaystyle \frac{\pi r^2h}{2\pi rh}=\frac{r}{2}=\frac{1650}{660}=2.5\)
\(r=5\) cm
\(\displaystyle 2\times\frac{22}{7}\times5\times h=660\), so \(\displaystyle \frac{220}{7}h=660\)
\(\displaystyle h=\frac{660\times7}{220}=21\) cm
