Introduction to Cross Sections

Q: Here are the shadows of some \$3-D\$ objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be many answers for these!).

Given,to identify different views of a \$3\$D objects.But,Assuming directly \$3\$ dimension views of a object is quiet difficult, so now inorder to find out the different views let us take a lamp and try to analyse the shades of every particular geometry figure thus given(i) circle.so when light is focused on to the circle we get a view of a sphere as shown below in figure.\$\therefore\$ The circle can we have different views like spherical or circular objects.(ii)Trinagle:when light is passed through triangle it looks like figure bview of triangle when light is focused on to it.Triangle can be viewed as a triangular prism.\$\ast\$ It can be viewed as a triangular shapes on right prism with triangular base.(iii) square:When light gets focused on to square it looks as figure.the view of square when light is passed through it\$\ast\$ A square looks like a cube or square sheets.(iv) Rectangle:When light gets focused on to rectangle it looks as figure.The view of rectangle will be as a cylinder when exposed to light.\$\ast\$ A rectangle looks like a cylinder or rectangular sheets.

Q: What cross-sections do you get when you cut a brick vertically?

When we cut a brick vertically then we get a rectangular cross-section. Hence, option (D) is correct.

Q: A bulb is kept burning just right above the ball. Name the shape of the shadow obtained.

The shadow will be a two dimensional figure.Since the bulb is just above the ball the shadow formed will be circular, as ball cuts off the light in a circular fashion.Thus, the shape of the shadow will be a circle.

Q: A cross section perpendicular to the base of a cylinder give us what two dimensional shape?

The cross-section perpendicular to the base of a cylinder given as a rectangular shape.

Q: What is the vertical cross-section of a solid cylindrical pipe shown in the figure?

The vertical cross-section of a solid cylinder is a rectangle.

Q: What is the cross-section view of triangular pyramid?

It is a triangular pyramid therefore the cross - section view is a triangle.

Q: What cross-sections do you get when you cut a brick horizontally?

Rectangular cross-section obtained if we cut a brick horizontally.

Q: A square pyramid is cut along the shaded plane shown in the figure. Which of the following is the cross-section of this solid?

If a square pyramid is cut along the shaded plane, then the cross - section of the solid is square. Because it is a square pyramid.

Q: The difference between a rectangle and a cube is

The difference in rectangle and cube is that, a rectangle is a \$2\$-dimensional figure where the length and the breadth of the geometry are specified. A cube is a \$3\$- dimensional figure where the length, breadth and depth of the geometry are specified.