# Agenda for today - PowerPoint PPT Presentation

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Agenda for today. New Solids: CYLINDERS, PYRAMIDS, CONES, SPHERES Challenge Questions Projects and exam area next week! Sites: 1 , 2 , 3 , mathsnacks.org Videos (Bubbles is #2): 1 , 2. Solids: Cylinders. Have 2 identical faces (bases) The two bases are circles

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Agenda for today

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### Agenda for today

New Solids:

CYLINDERS, PYRAMIDS,

CONES, SPHERES

Challenge Questions

Projects and exam area next week!

Sites: 1, 2, 3, mathsnacks.org

Videos (Bubbles is #2): 1, 2

### Solids: Cylinders

Have 2 identical

faces (bases)

• The two bases are circles

• The two bases lie in parallel planes

### Solids: Cylinders (cont'd)

Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases

SIXTH

PROBLEM

SET (from last time)

### Solids: Cylinders (cont'd)

Recall the formula for SA of a prism

Compare it to our cylinder formula

### Solids: Cylinders (cont'd)

Recall the formula for V of a prism

Compare it to our cylinder formula

Label a cylinder’s height and radius

Find the surface area of a prism

Find the volume of a prism

SEVENTH PROBLEM SET

### Solids: Cylinders (cont'd)

Discussion question:

• Which cylinder makes a better container?

### Pyramids (continued)

Have a polygon for a base

Have triangles that join the base to the apex

Have some tricky terminology…

### Pyramids (continued)

Height (also known as altitude) is the perpendicular distance between base and apex

Slant height is the distance between the apex and the center of the base’s edge

FIRST PROBLEM SET

### Pyramids (continued)

Here is the surface area formula:

P is perimeter of the base

S is slant height

BA is area of the base

### Pyramids (continued)

Here is the volume formula:

BA is area of the base

H is height (or altitude)

Correctly label a pyramid’s apex, base, height, and slant height

Find the surface area of a square pyramid

Find the volume of a square pyramid

SECOND PROBLEM SET

### Cones (continued)

Have a circle for a base

Have an apex

Have both height and slant height

“In projective geometry, a cylinder is simply a cone whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

### Cones (continued)

Here’s the formula for surface area:

“r” is radius of the base

“S” is slant height

### Cones (continued)

Here’s the formula for volume:

“H” is height (or altitude)

Correctly label a cone’s apex, base, height, and slant height

Find the surface area of a right cone

Find the volume of a cone

THIRD PROBLEM SET

### Spheres (continued)

Have the other

Circle stuff

Come up with the formula for SA…

### Spheres (continued)

Here is the surface area formula:

(This formula wierds me out: why is it so simple?)

### Spheres (continued)

Here is the volume formula:

(notice that r is cubed)

FOURTH PROBLEM SET

Find the surface area of a sphere

Find the volume of a sphere

Work with combinations

FIFTH PROBLEM SET

### Challenge Questions

Why do elephants have big ears?