Question

The formula below shows the relationship between the volume (v), in cubic centimeters, of a cylinder and the radius (r) and height (h), in centimeters, of the cylinder.

v = πr2h

The formula below shows the relationship between the diameter (d), in centimeters, of the circular base of the cylinder, and the radius, in centimeters, of the base.
d=2r

1. Express the volume of the cylinder in terms of its diameter and height.

Answer 1

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ d=diameter\\[-0.5em] \hrulefill\\ d=2r\\ (d)/(2)=r \end{cases}\implies V=\pi \left( \cfrac{d}{2} \right)^2 h \\\\\\ V=\pi \left( \cfrac{d^2}{2^2} \right)h\implies V=\cfrac{\pi d^2 h}{4}`