GAE - Volume Lesson

Volume

Volume is defined as the amount of space occupied by an object. In this lesson, we'll look at the volume of cones, cylinders, and spheres. Remember, volume is a three dimensional measurement and is, therefore, measured in cubic units.

Cones

image of cone What is the volume of a cone (in terms of $LaTeX: \Pi$ $\Pi$ ) whose height is 15 ft. and radius 9 ft.?

V = ¹/₃ equation image indicator $LaTeX: \Pi$ $\Pi$ r²h
V = ¹/₃ $LaTeX: \Pi$ $\Pi$ (9)²(15)
V = ¹/₃ $LaTeX: \Pi$ $\Pi$ (81)(15)

V = ¹/₃ equation image indicator $LaTeX: \Pi$ $\Pi$ (1215)

V = 405 equation image indicator $LaTeX: \Pi$ $\Pi$ ft.³

View the video Links to an external site. to see another example.

Cylinders

image of cylinder Find the volume of a cylinder(in terms of $LaTeX: \Pi$ $\Pi$ ) whose radius is 5 cm and whose height is 10 cm.

V = equation image indicator $LaTeX: \Pi$ $\Pi$ r²h
V = $LaTeX: \Pi$ $\Pi$ (5²)(10)
V = $LaTeX: \Pi$ $\Pi$ (25)(10)
V = 250 $LaTeX: \Pi$ $\Pi$ cm³

View the video Links to an external site. to see another example.

Sphere

image of sphere Find the volume of a sphere whose radius is 8 inches.

V= ⁴/₃ equation image indicator $LaTeX: \Pi$ $\Pi$ r³

V = ⁴/₃ equation image indicator $LaTeX: \Pi$ $\Pi$ (8)³
V = ⁴/₃ $LaTeX: \Pi$ $\Pi$ (512)
V = ²⁰⁴⁸/₃ $LaTeX: \Pi$ $\Pi$ in.³

V = 682 $LaTeX: \frac{2}{3}$ $\frac{2}{3}$ equation image indicator $LaTeX: \Pi$ $\Pi$ in.³

View the video Links to an external site. to see another example.

Homework

Now that you have spent some time learning about volume, you are ready to complete your Volume Homework. Click here to download the Volume Homework. Links to an external site.

Once you have completed the Volume Homework, check your even answers and make sure you ask your teacher if you have any questions. Links to an external site. When you feel confident in your work, you'll need to take the Volume Homework Quiz. Make sure you have your Homework completed when you log in to take it and remember this is a timed quiz.

IMAGES CREATED BY GAVS