Question

A piece of paper is used to make a cylinder (without a top and bottom) that is 8 inches long and has a radius of 1.5 inches. Assuming no part of the paper overlap’s, what is the area of the piece of paper? Show work

Answer 1

To find the area of the paper used to create the cylinder, multiply the height of the cylinder (8 inches) by the circumference (9.42 inches) to get 75.36 square inches.

Step-by-step explanation:

To calculate the area of the piece of paper used to make a cylinder without a top and bottom, we must consider the shape it would assume when flattened out. The paper would be rectangular, with one dimension being the height of the cylinder (8 inches) and the other being the circumference of the circle that forms the cylinder's side. The circumference of a circle is given by the formula C = 2πr. In this case, the radius r is 1.5 inches.

First, we calculate the circumference: C = 2π(1.5 inches) = 3π inches, which is approximately 9.42 inches (using π ≈ 3.14). Then, we calculate the area of the rectangle which is the height times the circumference, or 8 inches × 9.42 inches = 75.36 square inches. This is the area of the piece of paper needed to create the cylinder.

Answer 2

75.36

Step-by-step explanation:

Formula for circumference of circle is: πd

radius is half of the diameter so we have to multiply that by 2.

1.5*2=3

π in decimal form = 3.14

3*3.14=9.42

That is one side of the rectangle. The height of the rectangle is 8. Multiply the two sides.

9.42*8=75.36

The area of the rectangle is 75.36.

Hope this helps!

If not, I am sorry.