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# Agenda for today - PowerPoint PPT Presentation

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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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?

Solids: Pyramids

Have a polygon for a base

Have triangles that join the base to the apex

Have some tricky terminology…

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

Here is the surface area formula:

P is perimeter of the base

S is slant height

BA is area of the base

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

Solids: Cones

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) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Here’s the formula for surface area:

“r” is radius of the base

“S” is slant height

Cones (continued) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Here’s the formula for volume:

“H” is height (or altitude)

Cones whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”TASKS

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

Solids: whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”Spheres

Spheres (continued) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Have the other

Circle stuff

Come up with the formula for SA… whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Spheres (continued) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Here is the surface area formula:

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

Spheres (continued) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Here is the volume formula:

(notice that r is cubed)

FOURTH PROBLEM SET

Spheres whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”TASKS

Find the surface area of a sphere

Find the volume of a sphere

Work with combinations

FIFTH PROBLEM SET

Challenge Questions whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Why do elephants have big ears?