Cone It is a pyramid whose base is a circle Prism It is a solid - PowerPoint PPT Presentation

D AY 157 – C IRCULAR BASED P RISMS

I NTRODUCTION So far, we understand what a prism is. Most important, we can see images inform of a prism in real life situation. For instance, most of our rooms are inform of a prism, more boxes for carrying goods are informed of a prism among others. We can identify this due to a uniform cross-section. In case a cross-section is a circle, would it qualify to be a prism? In this lesson, we are going to identify the shapes of two-dimensional cross-sections(circular sections) of three-dimensional objects.

V OCABULARY Cross section A view of a figure when cut at any point along its length for objects with such features. Polygon A closed figure with 3 or more sides Prism A three dimensional object with a uniform cross section

Cone It is a pyramid whose base is a circle Prism It is a solid with a polygonal base which is also its cross section and rectangles along its height, or length.

Cylinder It is a solid with curved surface and a cross-section area that is a circle Sphere It is a solid whose shape is that of a ball. That is, all points on its surface are at equal distance from its center Pyramid It is a solid with a base and a curved or triangular surfaces along its height having a common apex.

Cylindrical prisms Prisms must have a uniform cross section throughout their length. This cross section can be any figure, whether a irregular or regular, polygonal or circular. So far, we have looked at a case where the cross section is polygon. If the cross section is circular, then we have only one case, a circular based prism which is actually a cylinder. 𝑚 𝑠

A cylinder is enclosed on sides by two circles that are equal and along its length/height by a curved surface which when cut along its length, we get a rectangle or a square whose radius is the length/height of the cylinder and length, the circumference of the circles at the end. When cut, we have the following image. 𝑚 𝑠 2𝜌𝑠 𝑠

Example Identify the number of circles that encloses a cylinder Solution The circle is the cross section of the cylinder hence it is at both ends of the figure. Hence, we have two equal circles

HOMEWORK When the curved surface of a cylinder is cut along a line parallel to its length, which figure(s) do we get?

A NSWERS TO HOMEWORK rectangle or a square

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