Pyramids and Cones — Worked Examples

A square pyramid has base side $6.00\,\text{m}$ and perpendicular height $9.00\,\text{m}$. Determine its volume.

A regular square pyramid has base side $8.00\,\text{m}$ and perpendicular height $6.00\,\text{m}$. Determine its face slant height and lateral area.

Use the pyramid from Example 2 to determine total surface area.

A right circular cone has radius $3.00\,\text{m}$ and perpendicular height $4.00\,\text{m}$. Determine its volume and slant height.

For the cone in Example 4, determine its lateral and total surface areas.

A right circular cone must hold $150\,\text{m}^3$ and has perpendicular height $8.00\,\text{m}$. Determine the required base radius.

A pyramid has base area $45.0\,\text{m}^2$ and volume $120\,\text{m}^3$. Determine its perpendicular height.

A cone has height $15.0\,\text{m}$ and base radius $6.00\,\text{m}$. Find the radius and area of a section parallel to the base located $9.00\,\text{m}$ from the apex.

For the cone in Example 8, what fraction of the full volume lies between the apex and the section $9.00\,\text{m}$ from the apex?

A uniform solid right circular cone is $12.0\,\text{m}$ high. Locate its centroid along the symmetry axis, measured from the base plane.

A right pyramid and an oblique pyramid have the same base area $B=28.0\,\text{m}^2$ and the same perpendicular height $h=9.00\,\text{m}$. The oblique pyramid has a longer apex-to-base-edge distance. Compare their volumes.

A right circular cone has original volume $24.0\,\text{m}^3$ and total surface area $30.0\,\text{m}^2$. Every linear dimension is enlarged by factor $k=1.50$. Determine the new volume and total surface area.