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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
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
Solids: Cylinders

Have 2 identical

faces (bases)

  • The two bases are circles

  • The two bases lie in parallel planes


Solids cylinders cont d
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 d1
Solids: Cylinders (cont'd)

Recall the formula for SA of a prism

Compare it to our cylinder formula


Solids cylinders cont d2
Solids: Cylinders (cont'd)

Recall the formula for V of a prism

Compare it to our cylinder formula


Cylinders tasks
Cylinders TASKS

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 d3
Solids: Cylinders (cont'd)

Discussion question:

  • Which cylinder makes a better container?


Solids pyramids
Solids: Pyramids


Pyramids continued
Pyramids (continued)

Have a polygon for a base

Have triangles that join the base to the apex

Have some tricky terminology…


Pyramids continued1
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



Pyramids continued2
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 continued3
Pyramids (continued)

Here is the volume formula:

BA is area of the base

H is height (or altitude)


Pyramids tasks
Pyramids TASKS

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
Solids: Cones


Cones continued
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 continued1
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 continued2
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 tasks
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 spheres
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
Spheres (continued) whose apex is at infinity, which corresponds visually to a cylinder in perspective appearing to be a cone towards the sky.”

Have a radius

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 continued1
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 continued2
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 tasks
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
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?

Seven Bridges of KonigsbergLink

Predict the Mobius strip’s split Link


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