Question

Determine a área total de um cone de 4 cm de raio e 6 cm de geratriz​

Answer 1

$\mathrm{Seja\ um\ cone\ com\ raio\ da\ base}\ r=4\ \text{cm}\ \mathrm{e\ geratriz}\ g=6\ \text{cm.}$

$\mathrm{A\ \acute{a}rea\ total}\ S\ \mathrm{da\ superf\acute{\i}cie\ do\ cone\ \acute{e}\ dada\ por}\text{:}$

$S=\pi r^2+\pi rg\Longrightarrow\boxed{S=\pi r(r+g)}$

$\Longrightarrow S=\pi(4)(4+6)=4\pi(10)\ \therefore\ \boxed{S=40\pi\ \mathrm{cm^2}}$