Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)

LO: To find surface area and volume of cylinders.

Know:

  • the formula for calculating the area of circles.

  • the formula for calculating the volume of prisms.

  • that the volume of a prism/cylinder can be found by multiplying the area of the base by the height.

Understand:

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

Do:

  • I can find the surface area and volume of cylinders.

Elaborations

  • analysing nets of cylinders to establish formulas for surface area

  • connecting the volume and capacity of a cylinder to solve authentic problems

  • determine the surface area of cylinders to solve problems.

Surface Area of Cylinders

A cylinder is basically made up of 3 shapes, the top, bottom and the side.

The top and bottom should be congruent (the same/identical) so we only need to calculate one of the sides then double that amount.
Area of top/bottom = ∏ x r x r
Area of side = 2 x ∏ x r x h
Formula: 2 x ∏ x r x r + 2 x ∏ x r x h


Volume of Cylinders

A cylinder is essentially a circular prism, so all we need to do is find the area of the circle then multiply it by the height.

Formula: ∏ x r x r x h

Problem Solving Tasks

  • Use the label and the plastic lid from a cylindrical container to help determine its surface area.

  • Compare the volumes of the two cylinders that can be created by taping the top and bottom, or the other two sides, of a standard sheet of paper.

Properties of Cylinders Videos

Next Lesson