New Solids: CYLINDERS, PYRAMIDS, CONES, SPHERES Challenge Questions Projects and exam area next week! Sites: 1, 2, 3, mathsnacks.org123 Videos (Bubbles is #2): 1, 212

Have 2 identical faces (bases) The two bases are circles The two bases lie in parallel planes

Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases SIXTH PROBLEM SET (from last time)

Recall the formula for SA of a prism Compare it to our cylinder formula

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

Discussion question: Which cylinder makes a better container?

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

FIRST PROBLEM SET

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

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.”

Here’s the formula for surface area: “r” is radius of the base “S” is slant height

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

Have a radius Have the other Circle stuff

Come up with the formula for SA…

Here is the surface area formula: (This formula wierds me out: why is it so simple?)

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

Why do elephants have big ears? Seven Bridges of Konigsberg LinkLink Predict the Mobius strip’s split Link Link