Obliczmy objętości piramidy Anny i piramidy Krzysztofa.

$V_{\text{A}}=36{\text{cm}}^2\cdot 8\text{cm}=288{\text{cm}}^3$  

$V_{\text{K}}={\left(8\text{cm}\right)}^2\cdot 6\text{cm}=64{\text{cm}}^2\cdot 6\text{cm}=384{\text{cm}}^3$  

 

$\text{I.}384{\text{cm}}^3-288{\text{cm}}^3=96{\text{cm}}^3\text{F}$  

 

Obliczmy masę piramidy Anny i piramidy Krzysztofa.

$m_{\text{A}}=288{\text{cm}}^3\cdot 2,5\frac{\text{g}}{{\text{cm}}^3}=720\text{g}$  

$m_K=384{\text{cm}}^3\cdot 3000\frac{\text{kg}}{{\text{m}}^3}=384{\text{cm}}^3\cdot 3000\cdot \frac{1000\text{g}}{{\left(100\text{cm}\right)}^3}=384{\text{cm}}^3\cdot 3000\cdot \frac{{\sout{1000}}^1\text{g}}{1000\sout{000}{\text{cm}}^3}=384\cdot \frac{3000}{1000}\text{g}=384\cdot 3\text{g}=1152\text{g}$  

`"II." \ \ "F" \ \ m_A  

$\text{III.}\text{F}1152\text{g}-720\text{g}=432\text{g}$

 

$\text{IV.}$  

Obliczmy długość krawędzi podstawy piramidy bazaltowej

$a^2=36{\text{cm}}^2\mid \sqrt{}$  

$a=\sqrt{36}\text{cm}=6\text{cm}$  

Korzystając z twierdzenia Pitagorasa obliczamy wysokości ścian bocznych obu piramid.

${\left(8\text{cm}\right)}^2+{\left(3\text{cm}\right)}^2=x^2$  

$64{\text{cm}}^2+9{\text{cm}}^2=x^2$  

$x^2=73{\text{cm}}^2\mid \sqrt{}$  

$x=\sqrt{73}\text{cm}$  

 

${\left(6\text{cm}\right)}^2+{\left(4\text{cm}\right)}^2=y^2$  

$36{\text{cm}}^2+16{\text{cm}}^2=y^2$  

$y^2=52{\text{cm}}^2\mid \sqrt{}$

$y=\sqrt{52}\text{cm}$  

 

$\sqrt{73}\text{cm}>\sqrt{52}\text{cm}$       

$\text{IV.}\text{P}$