Question

Please help urgent!

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 cylindera solid figure that has several curved surfacesA 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(HintThink about rolling a rectangular piece of paper into the shape of a cylinder.) Discuss your approach and why it works

Answer 1

The surface area of a cylinder is the surface area of rectangular piece of paper as you roll it into a cylinder and the surface area of the base and top areas:

Assume that you had a rectangular piece of paper with the long side h, and short side w, let h be the height of the cylinder as you roll it, the surface area generated is the circumference of the circle with radius r multiplied by the height = 2 ¶r h. The area of the top and bottom circular bases is 21 p².

The total surface area = 2 ¶rh+2¶r2 = 2

1r (h+ r) to express r in terms of w, w = 2 1r the width of the rectangle equal to the circumference of the circle, then the total surface area = w (h+ r)

but r = w/21, the surface area = w(h+w/ 21) = (wh+w2/21)