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 the surface of the prism?

Correct answer:

S =  4950 cm²

Step-by-step explanation:

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

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Savage Math Hacker 21

i think that all math is great but cubes graphic is better.????????

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Dr Math

graphics fixed

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