Question

A regular octagon base prism is cut out from a cylinder of base radius 7 cm and height (12+7✓2) cm. Find the volume of a prism ?

Answer 1

Answer:

$\text{volume of a prism }=(1372+1176\sqrt{2})\text{ cm}^3$

Step-by-step explanation:

A regular octagon base prism is cut out from a cylinder of base radius 7 cm and height (12+7✓2) cm.

First we find the area of base of octagon. Octagon has 8 sides. If we join the vertices of octagon to center then we get 8 isosceles triangle whose vertex angle is 45° because sum of 8 angles should be equal to 360°

Area of each triangle $=\dfrac{1}{2}r^2\sin\theta$

$\text{Area of triangle }=\dfrac{1}{2}\times 7^2\times \sin45^\circ$

$\text{Area of triangle }=\dfrac{49}{2\sqrt{2}}$

$\text{Area of base of prism }=8\times \dfrac{49}{2\sqrt{2}}=98\sqrt{2}$

Volume of prism = Base area x Height of prism

                          $=98\sqrt{2}\times (12+7\sqrt{2})$

                          $=1372+1176\sqrt{2}\text{ cm}^3\approx 3035\ cm^3$

Hence, The volume of the octagonal prism is    $(1372+1176\sqrt{2})\text{ cm}^3$