Octagonal Pyramid

Geometry Level 3

An octagonal pyramid is in a square prism whose base coincides with each other, as shown in the following figure. if the volume of square prism is $108 \text{ m}^3$ . what is the octagonal pyramid volume?

28 \text{ m}^3

36 \text{ m}^3

\frac{3}{2\sqrt{2}}\times180\text{ m}^3

84 \text{ m}^3

32 \text{ m}^3

1 solution

Chew-Seong Cheong
Sep 12, 2018

Let the side length of the square base be $3a$ and the height of the square prism by $h$ . Then the area of the square base is $A_s = 9a$ and its volume $V_s = A_sh = 9ah = 108$ $\implies ah = 12$ .

Now we note that the area of the octagonal base is $A_p = 7a$ and its volume $V_p = \dfrac 13 A_p h = \dfrac 13 \times 7 ah = \dfrac 13 \times 7 \times 12 = \boxed{28 \text{ m}^3}$ ,

Octagonal Pyramid

1 solution

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