School model

The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm ^ 3

Correct answer:

S =  14.4 dm²
m =  2.56 kg

Step-by-step explanation:

$$\begin{gathered} a=20\text{ cm } \\ h=24\text{ cm } \\ {S}_1=a^2=20^2=400{\text{cm}}^2 \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{24^2+(20\mathrm{/}2{)}^2}=26\text{ cm } \\ {S}_2={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{20\cdot 26}{2}}=260{\text{cm}}^2 \\ {S}_3=S_1+4\cdot S_2=400+4\cdot 260=1440{\text{cm}}^2 \\ S=S_3\to {\text{dm}}^2=S_3\mathrm{/}100{\text{dm}}^2=1440\mathrm{/}100{\text{dm}}^2=14.4{\text{dm}}^2={\displaystyle \frac{72}{5}}{\text{dm}}^2=14.4{\text{dm}}^2 \end{gathered}$$

$$\begin{gathered} \rho =0.8{\text{g/cm}}^3 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 400\cdot 24=3200{\text{cm}}^3 \\ {m}_1=V\cdot \rho =3200\cdot 0.8=2560\text{ g } \\ m=m_1\to \text{ kg}=m_1\mathrm{/}1000\text{ kg}=2560\mathrm{/}1000\text{ kg}=2.56\text{ kg}={\displaystyle \frac{64}{25}}\text{ kg}=2.56\text{ kg} \end{gathered}$$

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