Pyramid, cone কী?

Example 62.2 (Counting faces, edges, vertices)

A pyramid with a square base has $5$ faces ($1$ square $+ 4$ triangles), $8$ edges and $5$ vertices. With an $n$-sided base: $n + 1$ faces, $2n$ edges, $n + 1$ vertices. Check Euler’s little pattern: faces $+$ vertices $=$ edges $+ 2$.

Example 62.5

A pyramid has a square base of side $5$ cm and height $9$ cm:

1. base area: $B = 5^2 = 25$ cm$^2$;
2. volume: $V = \frac13 \times 25 \times 9 = 25 \times 3 = 75$ cm$^3$.

An ice-cream cone of radius $3$ cm and height $10$ cm:

Example 62.6 (Careful with the height)

For a cone, do not confuse the height $h$ (apex to center of the base, perpendicular) with the slant height $s$ (apex to the rim). They are related by Pythagoras (Theorem 58.1) in the right triangle apex–center–rim:

A cone with $r = 3$ and $s = 5$ therefore has height $h = \sqrt{25 - 9} = 4$, and volume $\frac13 \pi \times 9 \times 4 = 12\pi$.