Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (VCMMG365)

LO: To find surface area and volume of right pyramids.

Know:

  • the formula for calculating the area of 2-D shapes (triangles, squares, rectangles, parallelogram, kites, rhombuses, circles.)

  • the formula for calculating the volume of pyramids.

  • the definition of volume and surface area.

  • how to convert between different units of measurement eg.) mm to cm, cm to m and m to km include those involving 2 and 3 dimensions.

  • nets can be used to break down a 3-D shape into it’s 2-D shape parts specifically how the net of a pyramid is generated.

Understand:

  • That formulas can be used to quickly and efficiently to calculate the surface area and volume of pyramids.

Do:

  • I can find the surface area and volume of right pyramids and solve related problems.

Elaborations

  • using formulas to solve problems

  • using authentic situations to apply knowledge and understanding of surface area and volume

Right Pyramid

A right pyramid is a 3-D shape that has the apex (point of the pyramid) directly above the center of the base.

An oblique pyramid is a 3-D shape where the apex does not line up directly above the center of the base.


Volume of Right Pyramids

To find the volume of a right rectangular pyramid, you need to find the length, width and height then divide by 3.

Surface Area of Pyramid

To find the surface area of right prisms, first find the net of a 3-D shape, then calculate each individual section.

In this case, it’s pretty simple as the four triangular sides of the pyramid is identical, we only need to make 1 calculation then multiply it by 4 and add the base and you should have the total surface area of the pyramid.

One thing to remember is to use the slant height of the side of the pyramid and not the actual height of the pyramid as this is a common mistake that students always makes.

Surface Area and Volume of Right Pyramids Videos