# 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?

Result

S =  4950 cm2

#### Solution:

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

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