March 29: How do we find the surface area and lateral area of pyramids & cones? (AIM)

Aim: How do we find the surface area and lateral area of pyramids & cones?

• So like last time's review, the surface area is the outside of a solid. So here we'll be working with solids like pyramids & cones. The similarity between these two solids is that they both have triangle(s). 

• Pyramids have triangles as the lateral area and only one face. This face can be any shape, from a circle (cone) to a heptagon (7 sides). 

• A pyramid in general is a solid that connects a polygon base to a point, called the apex. 

• For the surface area & lateral area this is the formula. 

• But remember this is only for a square pyramid. For any base use the formula of 1/2pl (perimeter x slant length)  + B (area of the base). 

• For a cone it's the same, but its for a circular base. 

• Well that's about it. So try this problem !

What is the total surface area of this cone, rounded to 

the nearest tenth ?

Sources Cited: 

1. John Schnatterly AKA -->  http://johnschnatterly.blogspot.com/
2. http://www.mathsisfun.com/geometry/pyramids.html
3. http://www.mrlarkins.com/geometry/InteractiveTextbook/Ch10/10EM/PH_Geom_ch10_Review.html
4. http://hotmath.com/help/gt/genericprealg/section_9_5.html

March 28: How do we calculate the surface area of cylinders? (AIM)

Aim: How do we calculate the surface area of a cylinder? 

• To find the surface area of a any figure, you must have the right idea of what surface area is. 

• Surface area if one of the properties to a solid (which is 3-Dimensional). It covers the outside of the figure, unlike the volume (which is the inside).

• When calculating the surface area of a cylinder, you should remember that it's always easier to break the figure down into smaller shapes. For example:

So this figure shows
how there are 2
circles & a rectangle
in a cylinder.

• So for surface area you'll basically need the formula of a rectangle + 2 times the formula for a circle. Which gives you the SA formula. 

• So if that's how you find surface area, then how do you find lateral area? Well you basically just subtract the the bases. 

So lateral area is
the rectangle of
the cylinder. 

• Now that this is somewhat down-packed, try this problem. Don't worry its not hard ?! 

A cylinder has a radius of 8 inches and a height of 12 inches. What are the surface area of this cylinder?

1. SA = 320π
2. SA = 208π
3. SA = 480π

Sources Cited:

1. John Schnatterly AKA -->  http://johnschnatterly.blogspot.com/
2. http://www.mathsteacher.com.au/year8/ch10_geomcons/09_cones/cylinder.html
3. http://teamshen.blogspot.com/2010/04/how-does-surface-area-of-cylinder.html
4. http://www.mathguide.com/lessons/SurfaceArea.html