VOLUME OF CYLINDERS AND CONES

WARM UP

1. Find the length of a side of a square if the area is 64 cm².

2. Find the length of a cube if the volume is 8 inches².

3.

𝟏𝟔𝟗 4.

𝟑 𝟔𝟒

5. Find the distance between (1, 3) and (-2, 1).

Take a few minutes to write down what you know about volume.

https://www.youtube.com/watch?v=cYvw7_TrAXs&index=1&list=RDcYvw7_TrAXs

Today we are going to work at finding the formulas for volume of a cylinder and cone.

In your groups, use the NETS to help you discover the formulas.

• • •

build the cylinder and cone look at the basic shapes that make up a cylinder and cone use your prior knowledge of volume of prisms and area to help you

Volume of a Cylinder: A cylinder is made up of a base (circle) and a height (rectangle).

Volume of a rectangular prism: l Area of a circle:

𝝅𝒓 𝟐

(the base of a cylinder is circular)

∙

w

∙

h (l and w make up the base of the prism) V = h x b V = h x

𝝅𝒓 𝟐

Now, let’s perform an experiment to discover how the cylinder and cone are connected with regards to their volume.

Can you predict the volume of each figure? (given that each has the same diameter and height) Let’s look at the relationship between the cone and the sphere first.

Prediction: Actual:

https://www.youtube.com/watch?v=QnVr_x7c79w

Find the volume of the cylinder.

Find the volume of the cone: