A prism

A prism with an altitude of 15 cm has a base in the form of a regular octagon inscribed in a square of 10cm x 10cm. Find the volume of the prism.

Correct answer:

V =  1242.6407 cm³

Step-by-step explanation:

$$\begin{gathered} h=15\text{cm} \\ b=10\text{cm} \\ a+2\cdot a/\sqrt{2}=b \\ a+\sqrt{2}\cdot a=b \\ a=\frac{b}{1+\sqrt{2}}=\frac{10}{1+\sqrt{2}}\doteq 4.1421\text{cm} \\ S=b^2-a^2=10^2-4.1421^2\doteq 82.8427 \\ V=S\cdot h=82.8427\cdot 15=1242.6407{\text{cm}}^3 \end{gathered}$$

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