Question

Discussion Topic
In this unit, you calculated the surface area of solid figures composed of polygons, such
as rectangles and triangles. But imagine finding the surface area of a cylinder-a solid
figure that has several curved surfaces. A cylinder is made up of two circular bases and
a curved (lateral) surface in between Develop a formula for finding the surface area of
the outside of a cylinder based on what you know about the circumference of a circle
and the areas of circles and rectangles. (Hint: Think about rolling a rectangular piece of
paper into the shape of a cylinder.) Discuss your approach and why it works.

Answer 1

The formula for a surface area of a cylinder is  $2 \pi r^{2} + 2\pi rh$.

How do you develop a formula for finding the surface area?

For developing this formula you should consider that the surface area for a cylinder consists of the sum between the areas of circles and the rectangle, as shown in the image. Therefore, you have:

$Cylinder_{surface area}= 2 * area_{circle} + area_{rectangle}\\ \\ Cylinder_{surface area}= 2 * (\pi *r^{2} ) + (b*h)\\ \\ Cylinder_{surface area}= 2 \pi r^{2} + bh\\ \\ Cylinder_{surface area}= 2 \pi r^{2} + 2\pi rh$

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