When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: , where r is the radius. 

This means that we can directly solve for radius through substituting in the value for the area. 

Remember that you need to take the square root in order to solve for r. 

Therefore, the radius is 

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: , where r is the radius. 

This means that we can directly solve for radius through substituting in the value for the area. 

Remember that you need to take the square root in order to solve for r. 

Therefore, the radius is 

Your school as a circular lobby. If the distance around the outside of the lobby is , what is the distance across the widest part of the floor?

This question is asking us for diameter. We know this because we are told to find the distance across the widest part of a circular shape. The widest part of a circle will always go through the center, and assuming a straight line, will be its diameter.

To find the diameter, we can work backward from our circumference formula:

Now, we know that 

So, we can rewrite our C formula to get:

So, now we can solve for our diameter pretty easily!

So, our answer is:

First we need to recall that the formula for circumference of a circle is:

Where  is circumference and  is diameter

We are given the circumference, and told to use 3.14 for pi, so we can plug these into our equation and solve for diameter

we divide both sides by 3.14

Now that we have our diameter we need to divide it by 2 to find our radius 

Notice our answer is in ft because radius is linear

The radius is half of the diameter:

From here we plug in our diameter measure of 12 and solve for the radius:

The circumference of a circle can be found using this formula:

Where 

Substitute  and use , since we are rounding:

Round this to .

We will convert all linear distances to feet and all times to minutes.

The tires have diameter 30 inches, which is equal to  feet. Their circumference will be  times this, or  feet.

The car moves at a rate of 25 miles per hour, which is equivalent to 

 feet per minute.

The number of revolutions each tire makes is the distance traveled divided by the circumference of the tire, which is

.

Each tire revolves about 269 times in the course of one minute.

The equation of circumference of a circle can be found using . By substituting in our radius of 7 we can solve for C.

The equation for the circumference of a circle is , where  is the radius of the circle. The radius is half the diameter, or 5 inches.

The equation for circumference of a circle is .

Plug in the given radius value and solve: