Question

PLS HELP

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

Look at the unfolded cylinder down: it's consisted of a rectangle and 2 circles. so to find the surface area of the cylinder we should find the areas of the rectangle and the 2 circles.

1) A of 2 circles = 2(π
`r^(2)`) = 2π
`r^(2)`

2) A of rectangle = base x height (or length x width) = bh

but the if we fold the rectangle? what will happen?

the base will go around the circle, this means that the base is equal to the circle circumference, which is 2πr.

Therefore, A of rectangle = 2πrh

3) Surface area of cylinder = 2π
`r^(2)` + 2πrh

simplify more and take the common factor 2πr:

= 2πr (r+h)