Question

ANSWER ASAP PLEASE!!!!
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 paper into the shape of a cylinder.) Discuss your approach and why it works.​

Answer 1

Step-by-step explanation:

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 2 ¶ r2

The total surface area = 2 ¶ r h + 2 ¶ r2 = 2 ¶ r ( h+ r ) to express r in terms of w , w = 2 ¶ r the width of the rectangle equal to the circumference of the circle , then the total surface area = w ( h+ r )

but r = w / 2 ¶ , the surface area = w(h+w/ 2¶) = (wh+ w2/2¶)

Answer 2

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 2 ¶ r².

The total surface area = 2 ¶ r h + 2 ¶ r2 = 2 ¶ r ( h+ r ) to express r in terms of w , w = 2 ¶ r the width of the rectangle equal to the circumference of the circle , then the total surface area = w ( h+ r )

but r = w / 2 ¶ , the surface area = w(h+w/ 2¶) = (wh+ w2/2¶)

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