Learn to Find Surface Area, and Volume in Composite Solids by Subtracting Volumes and/or Areas.

You have a dough cube, and you puncture it with a pencil until the pencil protrudes by the opposite face of the cube, then you remove the pencil, and you are able to peek through the cylindrical hole. Would you be able to determine the volume of the cube after you have done the cylindrical hole? What do you need to do? Do you add volumes? Or do you subtract volumes? Could you calculate the surface area of the cube, including the interior area of the cylindrical hole?

The problems like the one above described are common in areas like building molds, architecture, engineering, and the construction industry. This lesson is an enrichment lesson to challenge you to go the extra mile, and solve surface area, and volume problems when you have to subtract a volume from another volume, and areas from the faces of the solids. You will be proud of yourself after you complete the lesson! If you try the suggested problems; you will be able to solve them with your stylus by clicking at the marker tools menu and selecting a pen, a marker, or the eraser.


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.

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

The union of the bases and the lateral surface.

Half of a sphere.

Lateral area.

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

Lateral surface
The surface not included in the base (s). 

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.

A polyhedron is a closed three-dimensional figure. All of the faces are made up of polygons.

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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