Circles Worksheets, Questions and Revision

) 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.

Because we’re finding the perimeter, we need to add up all side-lengths. This includes the big curved one and the straight one.

The straight one is made up of two radii, so its length is

5\times 2=10\text{ cm}

Now for the curved bit. It’s a semi-circle which is half a circle. Therefore, the curved bit of a semi-circle must be half the total circumference. The formula for circumference is \pi d and given that the radius is 5cm we must have the diameter to be 10cm. So, we get

\text{curved part }=(\pi\times 10)\div 2=15.707...\text{ cm}

Therefore, the perimeter is

10+15.707...=25.707...=26\text{ cm}\text{ (2sf)}

The formula for area is

\text{area }=\pi r^2

In this case, we have \text{area}=200 and r=x[\latex]. So, putting these values into the formula above, we get the equation</p> <p> </p> <p style="text-align: left;">[latex]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)}

The thing that’s different about this question is that we have to work backwards to find x. We know the formula we need is

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

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

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