Prism

Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?

Correct answer:

c =  15 dm
V =  5.766 hl

Step-by-step explanation:

$$\begin{gathered} S=448.88 \\ a=6.2 \\ {S}_1=a^2=6.2^2={\displaystyle \frac{961}{25}}=38.44 \\ S=2\cdot S_1+4a\cdot c \\ c=(S-2\cdot S_1)\mathrm{/}(4\cdot a)=(448.88-2\cdot 38.44)\mathrm{/}(4\cdot 6.2)=15\text{ dm} \end{gathered}$$

$$\begin{gathered} V_1=S_1\cdot c=38.44\cdot 15={\displaystyle \frac{2883}{5}}=576.6 \\ V=V_1\mathrm{/}100=576.6\mathrm{/}100=5.766\text{ hl} \end{gathered}$$

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