"Laura is painting a round floor cloth to resemble a globe for her bedroom floor. She wants to sew seam binding around the edges to keep the cloth from unraveling. If the radius of the cloth is 3 yards, how much binding should she buy?"
I dont understand the radius part of everything. Please help me.
The radius is half the diameter.
https://www.google.com/search?ei=uWeeXdrAKMzatQXqwoQ4&q=radius+circle&oq=radius+circle&gs_l=psy-ab.3..0i273j0l9.20169.27803..28131...3.4..0.118.1013.5j5......0....1..gws-wiz.......0i71j0i131j0i22i30.qArQkus6PAQ&ved=0ahUKEwiageORpZDlAhVMba0KHWohAQcQ4dUDCAs&uact=5
The circumference formula is
C = pi * 2r
The number π (pi) is defined as the ratio of the circumference to the diameter. π is approximately 3.14159...
C = πd
Now, the diameter is the distance across the circle. The radius is the distance from the center of the circle to the outside. So, d = 2r.
That means C = 2πr
In your case, C = 2π*3 = 6π = 18.85
For general questions like this, consult google first. You will find many discussions and videos.
the binding runs around the circumference of the circle.
Don't you have a formula that gives the circumference of a circle of radius r?
Yes, but I dont understand it. That's why I'm asking for help.
Thank you both! I think i understand it now.
Sure, I'd be happy to help explain the concept of radius and how it relates to this question.
In geometry, the radius of a circle is a line segment that connects the center of the circle to any point on the circle's circumference. It is represented by the letter "r" and is half the length of the diameter. In this case, the question states that the radius of the round floor cloth is 3 yards.
To understand why the radius is important in this context, we need to visualize how the floor cloth is shaped. Imagine a perfectly round piece of fabric, like a large circle. The radius is the distance from the center of the circle to any point on its edge.
In this question, the radius of 3 yards tells us the distance from the center of the floor cloth to the edge. This is useful because it allows us to determine the circumference of the floor cloth, which is the distance around the edge of the circle.
The formula to calculate the circumference of a circle is C = 2πr, where "C" represents the circumference and "π" (pi) is a mathematical constant approximately equal to 3.14.
Let's substitute the given radius, which is 3 yards, into the formula to find the circumference: C = 2π(3) = 6π.
Now we have the circumference of the round floor cloth, which is 6π yards. This represents the full length around the edge of the cloth.
To find out how much binding Laura should buy, we need to know the length of the binding she wants to sew around the edges. If, for example, she wants to sew the binding once around the entire circumference of the cloth, she would need to buy a binding length equal to the circumference. In this case, that would be 6π yards.
However, it's essential to consider any extra length needed for joining and securing the binding. So, Laura may want to add a few extra yards to ensure she has enough binding material.
Therefore, Laura should buy at least 6π yards of seam binding for the floor cloth, but she may want to consider getting slightly more to account for any additional requirements or mistakes during the sewing process.