Surface Area and Volume of a Pyramid
Today you will need:
Grab a warm-up from the wooden desk
Goals:
How do you know?
Review
Calculate the total and lateral surface area for each shape.
Cones and Pyramids
Based on what we know about Cavalieri’s Principle, what can we say about the volume of these two shapes?
Pyramids
A pyramid is a polyhedron with a polygonal base and lateral faces. The faces are triangles and they meet at a common vertex.
Surface area of a Pyramid
Find the surface area of the given pyramid.
What strategies did you use?
Surface area of a Pyramid
Find the surface area of the given pyramid.
What strategies did you use?
Surface area of a Pyramid
Find the surface area of the given pyramids. What strategies did you use?
Volume of a Pyramid
We can derive the volume formula of a pyramid from the volume formula for a rectangular prism just like we derived the formula for area of a triangle using what we know about the area of a rectangle.
Area of a square = b*h
Area of a triangle = ½*b*h
Volume of a Pyramid
Find the volume of the given pyramids.
What strategies did you use?
Volume of a Pyramid
Find the volume of the given pyramids.
What strategies did you use?
Tell me What you learned today?!
What I noticed…
What I wondered…
One connection I made was…
Independent Practice:
G16: Perimeter, Volume, Surface Area | |
Skills | Video Links |
Perimeter of Irregular Shapes | |
Area of Irregular Shapes | |
Volume of Rectangular Prism Visually | |
Volume of a Cylinder | |
Volume of Rectangular Prisms/Cylinders | |
Surface Area of a Cylinder | |
Surface Area of Rectangular Prisms | |
Volume of a Cone | |
Volume of a Pyramid | |
Surface Area of Square Pyramids | |
Volume of a Sphere (Level 1) | |
Delta Math G16: Perimeter, Volume, Surface Area
Delta Math Q4 Skill & Drill (due May 27)
Resources
Mod 8 Standards
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects, e.g., modeling a tree trunk or a human torso as a cylinder.
G.MG.2 Apply concepts of density based on area and volume in modeling situations, e.g., persons per square mile, BTUs per cubic foot.
G.MG.3 Apply geometric methods to solve design problems, e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios.
G.GMD.1 Given an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
G.GMD.5 Understand how and when changes to the measures of a figure (lengths or angles) result in similar and non-similar figures.
G.GMD.6 When figures are similar, understand and apply the fact that when a figure is scaled by a factor of k, the effect on lengths, areas, and volumes is that they are multiplied by k, k^2, and k^3, respectively.