Right cone surface and volume

Text

A right cone has base radius $5$ cm and height $12$ cm. Find the slant height, the lateral surface, the total surface and the volume.

Solution

Slant height: $a=\sqrt{r^2+h^2}=\sqrt{25+144}=13$ cm. Lateral surface: $S_\ell=\pi r a=\pi\cdot5\cdot13=65\pi\approx204.20$ cm$^2$. Total surface: $S_t=\pi r(r+a)=\pi\cdot5\cdot18=90\pi\approx282.74$ cm$^2$. Volume: $V=\dfrac13\pi r^2 h=\dfrac13\pi\cdot25\cdot12=100\pi\approx314.16$ cm$^3$. $\boxed{a=13\ \text{cm};\ S_\ell=65\pi;\ S_t=90\pi\ \text{cm}^2;\ V=100\pi\ \text{cm}^3}$