Pre-College MathClassifying Solids

PrismsPrisms are named for their base shape:

Rectangular PrismTriangular PrismHexagonal PrismPentagonal PrismOctagonal PrismTrapezoidal PrismSquare Prism

Prisms

Prisms are made up of two bases and rectangular faces connecting the edges of the bases two each other.

Cylinders

Cylinders have a circle for a base and one rectangular face curved around the circumference of the circle

Pyramids

Pyramids are named for their bases as wellRectangular PyramidTriangular PyramidHexagonal PyramidPentagonal PyramidOctagonal PyramidSquare Pyramid

Pyramids

Pyramids are made up of one base and triangles which converge at a point (vertex) opposite the base

Spheres and Hemispheres

Spheres are shaped like a round ball

A hemi-sphere is half a sphere

Cones

Cones have a circle for a base and a curved face that converges at a vertex opposite the base

HomeworkAssignment 10-6

Pre-College MathVolume of Prisms and Cylinders

What is volume?

The volume of a solid is the number of cubic units contained in its interior. Meaning how many cubic units it can “hold”.

The volume of an object is measured in cubic units (i.e. etc).

Volume of a Prism

The Volume of a Prism is found by taking the area of the base shape and multiplying it by the height if the prism

So the formula is: This works because you can think of

taking slices of the base shape and stacking them on top of each other

Some extras… Volume of a cube:

The volume of a cube is the cube of the length of its side:

Congruence:If two polyhedra (solid bounded by polygons)

are congruent, then they have the same volume

Volume Addition:The volume of a solid is the sum of the

volumes of all its NON-OVERLAPPING parts.

Helpful Hints

Area of a regular polygon:

Area of a rectangle:

Area of a triangle:

Volume of a Cylinder

This is the same as the volume of a prism with one little difference, the base is ALWAYS a circle

Therefore, the formula is:

HomeworkAssignment 10-7

Pre-College MathVolume of a Pyramid, Cone, and Sphere

Volume of a Pyramid

The Volume of a Pyramid is given by the area of the base of the pyramid times the height of the pyramid all divided by three

Thus, the formula is:

Volume of A Cone

The volume of a cone is given by the area of the circular base multiplied by the height od the cone, the whole quantity dived by three

Thus, the formula is:

Volume of a Sphere

The volume of a sphere is given by four thirds times pi times the radius of the sphere cubed (raised to a power of three).

Thus, the formula is:

HomeworkAssignment 10-8