$<br>$

$R=\frac{1}{2}a$

$h=\frac{a\sqrt{3}}{2}$

$r=\frac{1}{3}\cdot \frac{a\sqrt{3}}{2}=\frac{a\sqrt{3}}{6}$

$P_w=2R^2\Pi +2R\Pi \cdot h$

$P_w=2\cdot {\left(\frac{1}{2}a\right)}^2\Pi +2\cdot \frac{1}{2}a\Pi \cdot \frac{a\sqrt{3}}{2}$

 

$P_w=2\cdot \frac{1}{4}{a}^2\Pi +\frac{a^2\sqrt{3}}{2}\Pi =$ $\frac{1}{2}{a}^2\Pi +\frac{a^2\sqrt{3}}{2}\Pi =\frac{\Pi a^2\left(1+\sqrt{3}\right)}{2}$

 

$P_s=R^2\Pi +\Pi Rl$

$P_s={\left(\frac{1}{2}a\right)}^2\Pi +\frac{1}{2}{a}^2\Pi =\frac{1}{4}{a}^2\Pi +\frac{1}{2}{a}^2\Pi =\frac{3}{4}{a}^2\Pi$

$P_k=4\Pi r^2$

$P_k=4\cdot {\left(\frac{a\sqrt{3}}{6}\right)}^2\Pi$

$P_k=4\cdot \frac{3a^2}{36}\Pi$

$P_k=\frac{a^2\Pi }{3}$

Odp.Pole walca wynosi $\frac{\Pi a^2\left(1+\sqrt{3}\right)}{2}$ ,pole stożka $\frac{3}{4}{a}^2\Pi$ ,a pole kuli $\frac{a^2\Pi }{3}$ .