$V_{cubo}=l^3=12^3=1728~cm^3$
$S_{b,piramide}=l^2=10^2=100~cm^2$
$V_{piramide}=\frac{S_{b,piramide}*h}{3}=\frac{100*3,75}{3}=125~cm^3$
$V_{portacenere}=V_{cubo}-V_{piramide}=1728-125=1603~cm^3=1,603~dm^3$
$P=V*ps=1,603*3,3=5,3~kg$
$S_{l,portacenere}=S_{l,cubo}+S_{b,cubo}+(S_{b,cubo}-S_{b,piramide})+S_{l,piramide}$
Dove:
$S_{l,cubo}=4*l^2=4*12^2=4*144=576~cm^2$
$S_{b,cubo}=l^2=12^2=144~cm^2$
$S_{l,piramide}=\frac{2p*a}{2}$
$2p_{piramide}=4*l=4*10=40~cm$
$r=\frac{2S_{b,piramide}}{2p_{piramide}}=\frac{2*100}{40}=5~cm$
$a=\sqrt{h^2+r^2}=\sqrt{3,75^2+5^2}=\sqrt{14,0625+25}=\sqrt{39,0625}=6,25~cm$
--> $S_{l,piramide}=\frac{2p*a}{2}=\frac{40*6,25}{2}=125~cm^2$
$S_{l,portacenere}=S_{l,cubo}+S_{b,cubo}+(S_{b,cubo}-S_{b,piramide})+S_{l,piramide}=576+144+(144-100)+125=889~cm^2$