Question 3 options:
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
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