# 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 result:

c =  15 dm
V =  5.766 hl

#### Solution:

$S=448.88 \ \\ a=6.2 \ \\ S_{1}=a^2=6.2^2=\dfrac{ 961 }{ 25 }=38.44 \ \\ S=2 \cdot \ S_{1}+4a \cdot \ c \ \\ c=(S-2 \cdot \ S_{1})/(4 \cdot \ a)=(448.88-2 \cdot \ 38.44)/(4 \cdot \ 6.2)=15 \ \text{dm}$
$V_{1}=S_{1} \cdot \ c=38.44 \cdot \ 15=\dfrac{ 2883 }{ 5 }=576.6 \ \\ V=V_{1}/100=576.6/100=\dfrac{ 2883 }{ 500 }=5.766 \ \text{hl}$

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