Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?

Correct result:

S =  4950 cm2

Solution:

$V=20250 \ \text{cm}^3 \ \\ \ \\ V=abc=x \cdot \ 2x \cdot \ 3x=6x^3 \ \\ x=\sqrt[3]{ \dfrac{ V }{ 6 } }=\sqrt[3]{ \dfrac{ 20250 }{ 6 } }=15 \ \text{cm} \ \\ a=x=15 \ \text{cm} \ \\ b=2 \cdot \ x=2 \cdot \ 15=30 \ \text{cm} \ \\ c=3 \cdot \ x=3 \cdot \ 15=45 \ \text{cm} \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (15 \cdot \ 30+30 \cdot \ 45+15 \cdot \ 45)=4950 \ \text{cm}^2$

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