Cylinders and Circular Solids — Worked Examples

A circular pipe has internal radius $0.200\,\text{m}$ and length $10.0\,\text{m}$. Determine the internal geometric volume.

A closed cylindrical steel tank has radius $3.00\,\text{m}$ and height $8.00\,\text{m}$. Determine the total geometric surface area.

A cylindrical reservoir holds $500\,\text{m}^3$ when full. Its perpendicular height is $10.0\,\text{m}$. Determine the required internal diameter.

A steel pipe is $6.00\,\text{m}$ long with outer radius $R=0.300\,\text{m}$ and inner radius $r=0.260\,\text{m}$. Determine the steel volume.

Use the pipe from Example 4. If steel density is $7850\,\text{kg/m}^3$, estimate its mass.

An oblique circular cylinder has base radius $2.50\,\text{m}$, perpendicular height $7.00\,\text{m}$, and generator length $8.20\,\text{m}$. Determine its volume.

An oblique cylinder has generator length $L_e=8.00\,\text{m}$. A section perpendicular to the generators has perimeter $P_R=11.5\,\text{m}$. Determine the lateral area.

A right circular cylinder of radius $2.00\,\text{m}$ is cut by a plane so the minimum and maximum heights above the base are $3.00\,\text{m}$ and $7.00\,\text{m}$. Determine the retained volume under the planar cut.

For the standard cylindrical ungula geometry taught in the lesson, let cylinder radius be $r=3.00\,\text{m}$ and maximum cut height be $h=4.00\,\text{m}$. Determine its volume, curved cylindrical area, semicircular base area, inclined planar area, and total area.

A paraboloid of revolution has base radius $4.00\,\text{m}$ and height $6.00\,\text{m}$. Determine its volume and compare it with the circumscribing cylinder.

A right cone and a cylinder each have radius $2.00\,\text{m}$ and height $9.00\,\text{m}$. Compare their volumes.

A geometrically similar cylindrical tank is built with every linear dimension $1.25$ times the original. If the original total surface area is $80.0\,\text{m}^2$ and volume is $50.0\,\text{m}^3$, determine the new values.