When I teach how to find the surface area of cylinders I like to add a constant level of challenge and enjoyment to the lesson. Rather than repetitively calculating the surface area of a cylinder I introduce more complex cylindrical shapes.
To find the surface area of a cylinder students need to understand which parts make up the net. To demonstrate how the curved surface makes a rectangle I roll up a sheet of A4 paper into a hollow cylinder and open it. This helps students to see how the circumference forms the length of the rectangle and the width is the height of the cylinder.
The area of the two circles which form the base and top of the cylinder are connected to the top and bottom of the rectangle.
When calculating the area of the net I leave the individual areas in terms of pi. This prevents any rounding up errors. The total surface area of the cylinder is found by adding the three individual areas together.
When I teach this I typically work through the Q1 (shown below) for the students.
The class and I will work through Question 2 together and they will attempt the Question 3 independently. After checking their mini-whiteboards I’ll address any misconceptions at the front.
At this point we have worked through three questions and are about 18 minutes into the lesson. To add more challenge, I ask the class to find the area of the semi-circular prism.
To give a little help we discuss which faces make up the surface area and how to find their dimensions.
After about 5 to 8 minutes most of the class have completed the process and confidently present their workings to me on mini-whiteboards. The only misconception was to find the length of the curved face as the full circumference rather than half of it.
The most common successful approach for this question was to consider the individual areas of each face without connecting them as a net. Some students attempted to create a net but found it difficult connecting the inside curved face.
In the plenary I challenge students to find the surface area of a composite solid involving two cylinders. I asked the class to do this in their books as there was not enough space on their mini-whiteboards.
By this stage in the lesson nearly all the class were comfortable leaving the areas in terms π.
This was a challenging and fun lesson for the students. By the end of the lesson all students could find the surface area of a cylinder in terms of pi and most could solve problems involving composite cylindrical shapes.
The next lesson in the Circles, Cylinders and Circular Shapes unit goes on to problem solving with the volume of cylinders.
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