3D Geometry Questions

If you have a regular dodecahedron and you slice it in half along a plane that passes through the centres of opposite faces, what is the shape of the cross-section?

A regular dodecahedron is sliced by a plane passing through two opposite edges and not through any vertices. What is the shape of the cross-section?

When a cylinder is sliced by a plane parallel to its height and passing through the center, what is the shape of the cross-section?

A rectangle of length $14\text{ cm}$ and breadth $7\text{ cm}$ is rotated about its shorter side to form a cylinder. What is the volume (in ${\text{cm}}^3$) of the cylinder so generated? (Take $\pi =\frac{22}{7}$)

How many cubes of length 50 cm can be accommodated in a container of 5 m in length, 2 m in width and 5 m in height?

Find the maximum length of a rod, that can be placed in a room of dimension 12m×12m×14m.

A plane intersects a regular tetrahedron in such a way that the intersection forms an equilateral triangle. How many such planes can do this?

A cylinder is intersected by a plane inclined at an angle of $60^{\circ }$ to its axis. What is the shape of the resulting cross-section?

A sphere of radius $10\text{cm}$ is melted and made into a cone of height $10\text{cm}$. Find the diameter of the cone.