Calculate 2548

Calculate the volume of a wooden box in the shape of a prism with the base of a rectangle if the box's width is 8 dm, the length is 14 dm, and the size of the body diagonal is 25 dm.

Final Answer:

V =  2139.757 dm³

Step-by-step explanation:

$$\begin{gathered} a=8\text{dm} \\ b=14\text{dm} \\ d=25\text{dm} \\ {d}^2=a^2+b^2+c^2 \\ c=\sqrt{d^2-a^2-b^2}=\sqrt{25^2-8^2-14^2}=\sqrt{365}\text{dm}\doteq 19.105\text{dm} \\ V=a\cdot b\cdot c=8\cdot 14\cdot 19.105=112\sqrt{365}=2139.757{\text{dm}}^3 \end{gathered}$$

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