Question

The height of a right prism is $4$ cm. and its volume $8(2+1)$ c.c. If the base a regular octagon, find the length of a side (in cm).

Answer 1

Given : Height of prism $=4$ cm, Volume $=8(\sqrt{2}+1)$ cc

Let $a$ be the side of rectangular octagon

Area of base prism=Area of regular octagon $=2(1+\sqrt{2})a^2$

Volume of prism $=base\times height$

$Basearea=\frac{8(\sqrt{2}+1)}{4}$

$⟹2(1+\sqrt{2})a^2=2(\sqrt{2}+1)$

$⟹a^2=1$

$\therefore a=1$

Hence, length of a side of regular octagon is $1$ cm.