The tire of a toy car has a diameter of 9 cm. The inner wheel has a circumference of 6 pi cm. What is the area of the tire?

Question

A word problem of grade 9 geometry. It asks about area by giving the diameter and circumference. 

Answer 1

This problem is asking for the area of the tire, so we need to find the area of the outer circle of the tire and then subtract the area of the inner wheel.  

 

The area of a circle is represented by the equation, A = πr² (r = radius of the circle).

 

We can find the area of the outer circle of the tire by using the radius, which is half of the diameter, squaring it, and then multiplying it by π:

 

A = π(4.5)²

A = 20.25π

 

Now, we can find the area of the inner wheel by knowing that the circumference of a circle is represented by the equation, C = 2πr.  Because we know C = 2πr, we can solve for the radius:

 

6π = 2πr

6 = 2r

3 = r

 

So, the radius of the inner wheel is 3 cm.  We can now use this radius to find out the area of the inner wheel:

 

A = π(3)²

A = 9π

 

To find the area of the tire, we just have to subtract the area of the inner wheel from the area of the outer circle:

 

A = 20.25π - 9π

A = 11.25π

 

If we use 3.14 for π, then the area of the tire is 11.25(3.14) = 35.325 cm².

 

Answer 2

The concept area of a tire is a poor one, even if it's a toy car situation.

 

Let's assume that they're asking for the area of the sidewall of the tire, so this problem becomes the difference between the outer circle and the inner circle.

 

From the first given, we determine that the inner wheel's circumference of 6 pi means that the inner circle's diameter must be 6 cm because the formula for circumference is C = pi times diameter.  Therefore the inner circle's radius is 3 cm.

 

The outer circle's diameter 9 cm means that the radius of the inner circle must be 4.5 cm

 

So the question is answered by outer area - inner area = pi •4.5² - pi•3²

which I will let you calculate.  One thing I suggest is to use 3.1416 for pi, not a lesser inaccurate value such as 3.14 or 22/7.  Round to 1 or 2 decimal places, as your teacher dictates, BUT USE A MORE ACCURATE pi value during the calculations, in order to get the most accurate answer.