The regular

The regular quadrilateral pyramid has a volume of 24 dm³ and a height of 45 cm. Calculate its surface.

Correct answer:

S =  55.3954 dm²

Step-by-step explanation:

$$\begin{gathered} V=24{\text{dm}}^3 \\ v=45\text{ cm}\to \text{ dm}=45\mathrm{/}10\text{ dm}=4.5\text{ dm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot v \\ {S}_1=3\cdot V\mathrm{/}v=3\cdot 24\mathrm{/}4.5=16{\text{dm}}^2 \\ a=\sqrt{S_1}=\sqrt{16}=4\text{ dm } \\ {h}_2=\sqrt{v^2+(a\mathrm{/}2{)}^2}=\sqrt{4.5^2+(4\mathrm{/}2{)}^2}\doteq 4.9244\text{ dm } \\ {S}_2={\displaystyle \frac{a\cdot h_2}{2}}={\displaystyle \frac{4\cdot 4.9244}{2}}=\sqrt{97}{\text{dm}}^2\doteq 9.8489{\text{dm}}^2 \\ S=S_1+4\cdot S_2=16+4\cdot 9.8489=55.3954{\text{dm}}^2 \end{gathered}$$

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