Question

If the height of a cylinder is 4 times its circumference, what is the volume of the cylinder in terms of its circumference, C?

• A. $\frac{C^3}{\pi }$
• B. $\frac{{2C}^3}{\pi }$
• C. $\frac{{2C}^2}{{\pi }^2}$
• D. $\frac{{\pi C}^2}{4}$

Answer 1

Answer: (A)

$\frac{C^3}{\pi }$

Let height of the cylinder be h and circumference of cylinder be C.

$h=4\times C$ .... [Given](i)

$h=4\times 2\times \pi \times r$

$\therefore$ $r=\frac{h}{8\times \pi }$

$\therefore$ $r=\frac{4\times C}{8\times \pi }$ [From (i)]

$\therefore$ $r=\frac{C}{2\times \pi }$ .....(ii)

Volume of cylinder $=\pi$$r^2$h

$=\frac{2\times \pi \times r\times r\times h}{2}$ ... [Multiplying and dividing by 2]

$=\frac{C\times C\times 4\times C}{2\times 2\times \pi }$ [From (i) and (ii)]

$\therefore$ Volume of cylinder = $\frac{C^3}{\pi }$