ISEE Upper Level Quantitative Reasoning › How to find circumference
Find the circumference of a circle with a radius of 4cm.
To find the circumference of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know the radius of the circle is 4cm.
Knowing this, we can substitute into the formula. We get
The area of the shaded region in the above diagram is . Give the circumference of the circle.
The shaded region is an sector; this represents
of the circle. The area of the region is therefore
,
where is the radius. Setting
and solving for
:
The circumference of a circle is its radius multiplied by , or
You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .
What is the circumference of the crater?
You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .
What is the circumference of the crater?
To solve this, we need to recall the formula for the area of a circle.
Now, we know A, so we just need to plug in and solve for r!
Begin by dividing out the pi
Then, square root both sides.
Next, plug our answer into the circumference formula.
Let
Find the circumference of a circle with a radius of 8in.
To find the circumference of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know the radius of the circle is 8in.
We also know that.
Knowing all of this, we can substitute into the formula. We get
A circle has a radius of 5 miles, what is its circumference?
A circle has a radius of 5 miles, what is its circumference?
To find circumference, use the following formula:
Where r is our radius.
Plug in 5 miles to get our answer:
You want to ice skate around the outer edge of a circular pond (the water is frozen, because it is January and you live in Wisconsin). If the pond has a radius of 35 meters, how far will you skate in one lap around the pond?
Not enough information to complete.
You want to ice skate around the outer edge of a circular pond (the water is frozen, because it is January and you live in Wisconsin). If the pond has a radius of 35 meters, how far will you skate in one lap around the pond?
Let's begin by realizing what we are being asked for. They want us to find the total distance we will travel in one lap around the pond. This sounds like circumference, because we are going one full distance around the outside of the circle.
The formula for circumference is as follows.
Now, we have r, so just plug in and solve.
So, our answer is:
You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?
You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?
Begin with the formula for circumference of a circle.
Next, plug in our "r" and solve for C
So, we have our answer!
You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the circumference of the tree at chest height?
You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the circumference of the tree at chest height?
The formula for circumference of a circle is:
We have r, so simply plug it in and solve:
So, our answer is
Find the circumference of a circle with a diameter of 18cm.
To find the circumference of a circle, we will use the following formula:
where d is the diameter of the circle.
Now, we know the diameter of the circle is 18cm. So, we will substitute. We get
Find the circumference of a circle with a radius of 10in.
To find the circumference of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know the radius of the circle is 10in.
So, we get