Circles

The formula for circumference is \pi d, so we get

 

\text{circumference }=\pi \times 8.4=\dfrac{42}{5}\pi\text{ mm}

 

The circumference is the distance around the outside, so its units are the same as those of the diameter.

 

b) The formula for area is \pi r^2, so firstly we have to get the radius by halving the diameter:

 

r=8.4\div 2=4.2

 

Then we get

 

\text{area }=\pi \times 4.2^2=55.417...=55.4\text{ mm}^2\text{ (3sf)}

 

Area of shapes is always measured in “squared” units. Circles are no exception.

\text{Area}=\pi r^2 = \pi \times 5^2= 25\pi \text{ cm}^2

The formula for area is

 

\text{Area }=\pi r^2

 

In this case, we have \text{area}=200 and r=x. So, putting these values into the formula above, we get the equation

 

200=\pi x^2

 

We can now rearrange this equation to find x. Firstly, divide by \pi to get

 

\dfrac{200}{\pi}=x^2

 

Then, to find out the value of x, square root both sides

 

x=\sqrt{\dfrac{200}{\pi}}=7.97...=8.0\text{ cm (1dp)}

We know the formula we need is

\text{Circumference }=\pi d

We also know that the circumference is 120 and d is, in this case, x. So, filling it in those things that we have into the formula, we get

120=\pi \times x

Now we have an equation we can solve. We want x, so if we divide both sides by \pi, we get

\dfrac{120}{\pi} = x

Put this into a calculator and we get: x=38.2 cm, to 3sf.