Geometry

# Volume - Pyramid

Suppose the pyramid in the above diagram has a square base with side length $$8\text{ cm}.$$ If the volume of the pyramid is $$320\text{ cm}^3,$$ what is its height in $$\text{cm}?$$

If $$x=6,$$ $$y=10$$ and $$z=\sqrt{136},$$ what is the volume of the rigid body which can be formed by the above planar figure?

Note: The above diagram is not drawn to scale.

If a regular octahedron is inscribed in a sphere with radius $$r=8,$$ as shown above, what is the volume of this regular octahedron?

What is the volume of the above tetrahedron with six identical edges of length $$5 ?$$

If $$x=6,$$ $$y=16,$$ and $$z=11,$$ what is the volume of the water contained in the box, given that the water just touches the corner at $$B$$. Give your answer in $$\text{cm}^3 ?$$

The above diagram is not drawn to scale.

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