Question

The container was covered in plastic wrap during manufacturing. How many square inches of plastic wrap are used to wrap the container? (Right answers in terms of π.)

A)2πr^2 , where r is the radius of the container.
B) πr^2 +2πrh, where r is the radius and h is the height of the container.
C) πd ^2 , where d is the diameter of the container.
D) 4πr^2 , where r is the radius of the container.

Answer 1

The total amount of plastic wrap used to cover a cylindrical container in square inches is option B) πr² + 2πrh, which covers both the top and bottom circles and the rectangular side of the container.

Step-by-step explanation:

The question asks about the amount of plastic wrap used to cover a container in terms of square inches. This is a geometry problem involving the surface area of a cylinder (assuming the container is cylindrical as the question references radius). To cover a cylinder with plastic wrap, you would need to cover the top and bottom circles, and the rectangular side that wraps around the cylinder.

The formula for the area of a circle is A = πr². Since the container has two circular ends, you would use 2πr² to address the top and bottom areas. The side of the cylinder can be unfolded into a rectangle with the height h and the width equal to the circumference of the circles, which is 2πr. Therefore, the area of the rectangular side is 2πrh. Adding the two areas together, the total amount of plastic wrap in terms of the radius (r) and height (h) of the container is B) πr² + 2πrh.