Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)
LO: To find surface area and volume of cylinders.
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.
That formulas can be used to quickly and efficiently to find the surface area and volume of cylinders.
I can find the surface area and volume of cylinders.
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.