Volume of Geometric Solids

Geometry Regular ProgramSY 2014-2015

Sources:

Discovering Geometry (2008) by Michael Serra

Geometry (2007) by Ron Larson

The Geometric Solids

These solids take up space.

What is VOLUME?

It refers to the measure of

the amount of space

contained in a solid.

The Geometric SolidsWhat is

VOLUME?

It refers to the measure of

the amount of space

contained in a solid.

It is measured in cubic units.

Example:

How many cubes of cubic unit can fit inside the solid?

Example:

How many cubes of cubic unit can fit inside the solid?

Example:

How many cubes of cubic unit can fit inside the solid?

So how do we determine the volume of a solid?

It takes 3x3 cubes to cover the base area.

It takes 3x the base area to fill up the whole solid.

You need the base area h times. Base area

Height h

VOLUME OF SOLIDS

PRISMV = Base area x Height of prism

CYLINDERV = Base area x Height of cylinder

Exercises on VolumeSolve for the volume of each solid

Exercises on VolumeSolve for the volume of each solid

Exercises on VolumeSolve for the volume of each solid

Try these!Which has a greater volume?

Try these!Which has a greater volume?

Try these!Which has a greater volume?

Try these!Solve for the volume of each solid

Try these!Solve for the volume of each solid

How about the volume of a pyramid?

https://www.youtube.com/watch?v=OUDjY6vJ8pw

VOLUME OF SOLIDS

PYRAMIDV = One-third of the volume of the prism with same base and height

How about the volume of a cone?

https://www.youtube.com/watch?v=0ZACAU4SGyM

VOLUME OF SOLIDS

CONEV = One-third of the volume of the cylinder with same base & height

VOLUME

PRISM x

CYLINDER

x

PYRAMID

x

CONE x

SUMMARY: VOLUME

Exercises on VolumeSolve for the volume of each solid

Exercises on VolumeSolve for the volume of each solid

Exercises on VolumeSolve for the volume of each solid

Extra Exercises on VolumeSolve for the volume of each given solid

Extra Exercises on VolumeSolve for the volume of each given solid

Extra Exercises on VolumeSolve for the volume of each given solid

Extra Exercises on VolumeSolve for the volume of each given solid

Extra Exercises on VolumeSolve for the volume of the liquid.

Extra Exercises on VolumeSolve for the volume of the liquid.

Extra Exercises on Volume

Extra Exercises on Volume (seatwork) Solve the following:

1. Find the volume of an oblique prism inclined 45o from the base, if the area of the base is 20 cm2

and the lateral edge is 15 cm.

2. Find the volume of a right cylinder with a cylindrical hole if the larger radius is 10 inches, the smaller radius is 8 inches and the height is 9 inches.