G-Algebra Cylinders and Cones U9L2/L3

Volume of Cylinders(U8L2) & Volume of Cones(U8L3)

WAGNER/MONTCLAIR

4/19/2023

​Today's Objective:

8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

G-Goals

SWBAT develop and apply the formula for the volume of a cone to solve real world and mathematical problems.

G-Point

The volume of a cone is 1⁄3 the volume of a cylinder with equal height and radius

Cylinder Volume

​G-Algebra Terms (Record in notes)

​• Area – the size of a surface; the amount of space inside the boundary of a two-dimensional object.

• Base – the surface on which a solid object stands.

• Volume – the measure of the amount of space inside a three-dimensional solid.

• Radius – the distance from the center to the edge of a circle.Half of diameter

• Height (Altitude) – the vertical distance of a polygon of solid figure measured perpendicular from the base of the figure to the top.

• Diameter – any straight line segment that passes directly through the center of a circle.

• Circumference – the distance around a circle; the perimeter of a circle.

Multiple Choice

Find the volume of the cylinder in terms of  $$\pi$$  .

• $$96\pi\ cm^3$$  

• $$48\pi\ cm^3$$  

• $$144\pi\ cm^3$$  

• $$32\pi\ cm^3$$  

Working Backwards

Answer: 3 units

Answer = 4 inches

Volume of Cones!

• Remember, a pyramid was 1/3 the volume of a prism with the same base and height

• A cone is like a pyramid with a round base

• A cone is 1/3 of the volume of a cylinder with the same base and height too!

• You can also find the cylinder volume and divide by 3.

Multiple Choice

The cylinder and the cone here have the same base radius and height.

The volume of the cone is

$$9\pi\ units^3$$ .

What is the volume of the cylinder?

• $$3\pi\ units^3$$  

• $$9\pi\ units^3$$  

• $$27\pi\ units^3$$  

• Impossible to tell

That's all, Folks!

Get ready for your Pop Quiz

Review the notes YOU should've took and you will be fine.

No talking during quiz . If you talk, automatic F, automatic phone call. No exceptions.

LOCK IN GANG AND GOOD LUCK !!!!