Question

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

Answer:If you "unroll" a cylinder, you have a rectangle. Take a piece of  paper, like it says. You know how to find the area of it. Now roll it like s cylinder. How does it compare??

Explanation:                  Mark me as brainliest if you get it right

Answer 2

The surface region of a cylinder is the floor region of rectangle piece of paper as you roll it right into a cylinder.

The floor region of the bottom and pinnacle areas:

Assume which you had a square piece of paper with the lengthy aspect h, and quick aspect w, permit h be the peak of the cylinder as you roll it, the surface region generated is the circumference of the circle with radius r extended via way of means of the peak = $2 \pi r h$. The region of the pinnacle and backside round bases is $2 \pi r^{2}$

The overall surface region = $2 \pi r h + 2 \pi r^{2} = 2 \pi r ( h+ r )$  to specific 'r' in phrases of w, $w = 2 \pi r$ the width of the rectangle same to the circumference of the circle, then the overall surface region = w ( h+ r )

however  $r = w / 2 \pi$, the surface region = $w(h+w/ 2\pi ) = (wh+w^{2} /2\pi )$