# Hollow Cylinder

## Hollow Cylinder

Cylinder in which the bases are congruent annuli.

### 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}