How You Can Find Surface Area, and Volume in Composite Solids by Adding and/or Subtracting Volumes and/or Areas.

Your little sister is playing by the beach. She takes a cylindrical bucket and fills it with wet sand. She turns it upside down to dump the sand in the ground, and this keeps the shape of the bucket. She takes now a mold in the form of a cone and do the same; but dumping it on top of the cylinder she formed before. Finally with a scoop; she carves a tunnel through the cylinder. The tunnel has entrance, and exit. You dad knows that you are taking your geometry class, and then he asks you to find the volume of sand used by your little sister. You mom adds that she wants the surface area. Would you be able to do it?

In real life that happens in many industries. You use many plastic pieces in different shapes, those pieces were formed by injecting hot liquid plastic into the cavity of a mold; then cold water in the walls of the mold was circulated to cool down the piece and solidify it. The process to build the molds is not different of what your little sister might have done in the sand. In this lesson you will be able to calculate surface area, and volume of pieces that are formed by solids like cylinders, prisms, pyramids, and spheres, or hemispheres. The task will always consist in adding and/or subtracting areas, and volumes. This enrichment activity will really translate in a huge volume of opportunity to learn!. As with all other lessons you will be able to resort to sketch the solution or do the full solution of the problems. For that, use the MARKER TOOLS menu at the top of the screen. If you don't have a stylus you may use your finger to write on the screen (most market available tablets now allow it).

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

It is a 3-D figure with circular base, a vertex not in the plane of the circle, and has a curved surface connecting the base with the vertex. The altitude of the cone is the perpendicular segment that goes from the vertex to the plane containing the circle at the base. The height is the length of the altitude. The slant height is the length of the distance from the vertex to the edge of the base. For a right cone it is necessary that the altitude contains the center of the circle at the base.

Conic solid
The set of points between a point (the vertex) and a non-coplanar region (the base), including the point and the region.

The union of the bases and the lateral surface.

Cylindrical surface
The surface of a cylindrical solid whose base is a circle.

Half of a sphere.

Lateral area.

Lateral area
The area of the lateral surface of a solid.

Platonic solid
A Platonic solid is defined as a solid in which all of its faces are congruent regular polygons and the same number of regular polygons meet at each vertex.

It is a polyhedron that has two congruent and parallel faces, called bases. The remaining faces, which are parallelograms are called lateral faces. The altitude is the perpendicular segment whose endpoints are at the bases. The length of the altitude is the height of the prism. A right prism is one with all lateral faces rectangles. An oblique rectangle has some to be nonrectangular. 

It is a polyhedron whose base is a polygon and whose lateral faces are triangles with a common vertex called the vertex of the pyramid. The perpendicular segment whose endpoints are at the base and at the vertex of the pyramid is the altitude, which is the height of the pyramid. A regular pyramid has congruent isosceles triangles in the lateral faces and a regular polygon in the base. The length of the height for the lateral triangles is the slant height for the pyramid.

Regular pyramid
A pyramid whose base is a regular polygon and whose vertex forms a segment with the center of the polygon perpendicular to its plane.

Slant height
The length of a lateral edge of a conic solid.

Right prism
A prism whose direction of sliding is perpendicular to the plane of the base.

A sphere is properly defined as the set of points in the space that are equidistant of one point called center. Planes that go through the center of the sphere, intersect GREAT CIRCLES. The circumference of the sphere is the perimeter of any of its great circles.

The boundary of a 3-D figure.

Surface area
The total area of the surface of a solid.

Unit cube
Unit of measuring volume.



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