Surface Area Total area on the surface of the figure, amount of paper needed to cover it
Define 3D Figures Prism bases defines name of shape, sides are all rectangles 2. Cylinder bases are circles connected by a rectangle 3. Pyramid One base, this dictates name, all sides are triangles that meet at one point 4. Cone Pyramid with a circle for a base Sphere A circle rotated 360 degrees around one diameter
Net Unfold the 3D Figure to get a 2D blueprint, this may help you determine areas of all the shapes that make up the figure. Are there other Nets for this 3D figure?
Nets of Solids Try to draw the 3D figure Prisms Pyramids Cylinders Cones Spheres 2. Try to draw the nets for the following 3D figures
Parts of Solids Prisms – bases are the same, rectangles attach bases Pyramids – one base all sides are triangles
Steps to find Surface Area Works for Prism, Pyramid or Cylinder Draw a net and label the dimensions Calculate the area of each face and base Add all areas together Or If Prism Find perimeter of base and multiple by height Find area of base and double it Add two answers together
Example
Prisms For all prisms finding the surface area is the same, should have 2 bases the same and sides are all rectangles (could be congruent), unless prism is tipped (sometimes have opposite sides congruent so really only need to find 3 areas) This even works for cylinders
Examples Knowing that the circumference of the circle is the length of the rectangle
Pyramids Slant height – height of the triangular face of the pyramid Height – is a perpendicular segment from vertex to base
Pyramid
Cones Pyramid with a circular base, the face is not a triangle
Example
Summary Prism – area of 2 bases plus area of all faces Pyramid – area of the base plus area of all triangles, half the perimeter of base times slant height plus apothem Cylinder – area of 2 circles, circumference of circle times height at them together Cone – area of the circles plus slant height times radius times radius
Homework Pg 466 1, 3-9 Due next class Pg 524 2-22 Due Wed