Hollow Cylinder

Formulas

• The area A of a hollow cylinder is equal to the sum of the areas of its two bases (annuli), the lateral interior area \(A_1\) and the exterior area \(A_2\) :

\(\begin{aligned}
A&=A_b + A_1 + A_2 \\
&=2\left(πr_{\scriptsize{2}}^2-πr_{\scriptsize{1}}^2\right) + 2πr_{\scriptsize{1}}h  + 2πr_{\scriptsize{2}}h \\
&=2π\left( r_1+r_2 \right) \left(r_2-r_1+h\right)
\end{aligned}\)

• The volume V of a hollow cylinder is equal to the volume of the cylinder with radius \(r_{\scriptsize{2}}\) from which we subtract the volume of the cylinder with radius \(r_{\scriptsize{1}}\) :

\(\begin{aligned}
V&=πr_{\scriptsize{2}}^2h-πr_{\scriptsize{1}}^2h \\
&= πh\left(r_{\scriptsize{2}}^2 – r_{\scriptsize{1}}^2\right) \\
&= πh\left(r_{\scriptsize{1}}+r_{\scriptsize{2}}\right)\left(r_{\scriptsize{2}}-r_{\scriptsize{1}}\right)
\end{aligned}\)