If the height of the cylinder is $4$ times of its circumference what is the volume of cylinder in terms of circumference?
a). $\dfrac {C^3}{\pi}$
b). $\dfrac {2C^3}{\pi}$
c). $\dfrac {2C^2}{\pi^2}$
d). $\dfrac {\pi h^2}{4}$
My Attempt:
$$h=4C$$ Now, Volume$=\pi r^2 h$ $$=\pi r^2 C$$. ??
The circumference of the cylinder is given by $C= 2 \pi r$. From this we can write $r= \frac C{2 \pi }$.
Now, substitute $h=4C$ and $r= \frac C{2 \pi }$ into the volume expression $V= \pi r^2 h$ to obtain the required expression.