Question 3 options:

Question

If a cardboard tube is cut vertically, it is a rectangle. What is the surface area of a cardboard tube that is 4 inches long with a circumference of 5 inches?



Blank Space__________in²

Answer 1

To find the surface area of a cardboard tube, we need to find the area of the rectangle that is formed when the tube is cut vertically.

The length of the cardboard tube is given as 4 inches, and its circumference is given as 5 inches.

To find the width of the rectangle, we can use the formula for the circumference of a circle:

circumference = 2πr

where r is the radius of the circle (which is half the width of the rectangle).

In this case, the circumference is 5 inches, so we can solve for the radius:

5 = 2πr

Dividing both sides by 2π, we get:

r = 5/(2π)

Now, we can use the formula for the area of a rectangle:

area = length * width

The length is given as 4 inches, and we just found the width (which is the radius of the circle), so:

area = 4 * (5/(2π))

Simplifying this, we get:

area = 20/(2π)

This can be further simplified as:

area = 10/π

So, the surface area of the cardboard tube is:

Blank Space: 10/π in²