Area/Volume/Surface Area
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Here is a flat rectangle
Area of the base equals length times width
Let’s make it 3 dimensional
Area, base times height
Volume into it?
A pyramid, a special case, a square base
That volume equals 1/3 B times height
A surface area - the outer space
Add the area of all the sides
Chorus:
First we identify the base
Is this a circle, square, or a rectangle?
Once we know, we find the area for that shape
Multiply the base times the height
To get the volume of 3 dimensional prisms
Base: length times width
But for circular cylinders
We’ll be needing pi
I have a flat flat circle
Area of the base equals pi r squared
Lets make it 3 dimensional
Volume equals base times height
Filled with air
A cone, a special case, a circular base
That volume equals 1/3 B times height
Surface area, the outer space
Add the area of all the sides
To find the surface area:
Of a cylinder - 2 pi r squared + 2 pi r (height)
A rectangle - 2 (length times width) + 2 (height times width) + 2 (length times height)
Now a cone - pi r squared + pi r (l)
L is length, not height
Yea a pyramid - take the base
Add 2 times a side times the l just right
We have another flat circle
Area of the base equals pi r squared
This sphere is 3 dimensional
Volume 4/3 pi r cubed
Filled with air
2 cones in there that share a circular base
That’s only part of what can fit inside
Surface area all around the space
4 pi r squared, will cover what is outside