Lesson video

Am Mr. Lund and in this lesson, we're going to be working out the area of circles.

Hi everyone.

Hope you're excited to find out one of the most important mathematical formulas.

That is the formula to find the area of the circle.

Here's the formula.

The area of a circle is equal to pi multiplied by the radius, multiplied by the radius again.

Let's use algebra to simplify our formula.

The area of a circle is equal to pi times by r times by r.

We can simplify that further.

A is equal to pi r squared.

This is a formula to work out the area of a circle.

You need to memorise this for your exams. Estimates are really good way of checking your answers before you put them in a calculator.

Let's say that radius of this circle is six centimetres.

And let's say pi is around about three.

Which of these choices would be the best estimate for the area of this circle? Here's our formula, area is equal to pi r squared.

Let's substitute our values in.

Area is around about three.

That's the number we've used for Pi, times by six squared.

So the radius squared.

So A is around about 108 centimetre squared.

Have a look at this question.

Which gives the exact area of the circle? Here's your options.

When we are asked to find the exact area of a circle, it means we need to show our answer in terms of pi.

Let's have a look at that formula again.

Area is equal to pi r squared.

Let's substitute our values into our formula.

Remember here we have the diameter of 20 centimetres.

So having that we'll find the radius, which is 10 centimetres.

Area is equal to pi times by 10 squared.

10 squared is a hundred.

So we could just write, A is equal to a hundred pie centimetres squared.

Don't forget your units.

Here's some questions for you to try.

Pause the video and return to check your answers.

Here's the solutions to question number one.

In question one be a nine sixteenths of pie, could it be written like this.

Okay? Find the area of this circle to three significant figures.

Here's our formula.

What's the radius? r is 14 centimetres.

Let's substitute that value into our formula.

Area is equal to pie times by 14 squared.

Using a calculator, here is the answer I get.

Rounding to three significant figures, the area of this particular circle is 616 centimetres squared.

Don't forget your units.

Here's the question for you to try.

Pause the video and return to check your answers.

Here is the solution to question number two, and question two B.

You could have placed your fraction in a calculator like so with brackets around.

Okay.

well, let's see if you can find out what mistake Clare has made and how that goes getting along.

Pause the video, check your answers when you return.

Here are the solutions to questions three and four.

In question four, the answer has been rounded to two significant, sorry to three significant figures.

If you can find the area of a circle, then it's easy to find the area of a semicircle.

Area is equal to pi r squared.

So the area in this case is pi times by the radius squared.

Our diagram shows a diameter of 20.

So let's have it to find 10.

The radius is 10.

A is therefore equal to 314.

159, et cetera.

The area of the semicircle would be half of that value.

That would go to three significant figures, you should have an answer of 157 centimetre squared.

Well done for getting this far.

Pause the video and return to check your answers.

Well done for getting this far.

Here are questions five and six.

In question six, the compound shape, you could have drawn has two separate shapes.

Notice the width of the rectangle is the diameter of this semicircle.

Okay.