Prism - box

The prism's base is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.

Correct answer:

S =  570 cm²

Step-by-step explanation:

$$\begin{gathered} a=7.5\text{cm} \\ u=12.5\text{cm} \\ V=0.9{\text{dm}}^3\to {\text{cm}}^3=0.9\cdot 1000{\text{cm}}^3=900{\text{cm}}^3 \\ b=\sqrt{u^2-a^2}=\sqrt{12.5^2-7.5^2}=10\text{cm} \\ c=V/(a\cdot b)=900/(7.5\cdot 10)=12\text{cm} \\ S=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (7.5\cdot 10+10\cdot 12+7.5\cdot 12)=570{\text{cm}}^2 \end{gathered}$$

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