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Hello, my name is Mr. Chan, and in this lesson, we're going to learn about surface area and further problem solving.

Here's an example of the kind of problem that we might face when we're dealing with surface area.

So in this example, we're told that the surface area of a cone is 96 pi centimetres squared.

We've got to try and work out the radius of the cone, and we can see a diagram of the cone there with the radius and a slanted height of 10 centimetres.

So let's think about what we know in terms of the surface area of a cone.

Well, the surface area of a cone is given by the formula pi r squared plus pi rl, where l is the slope height of the cone, and we know that that's 96 pi because the question has told us that.

So we can create an equation to make those two equal.

So we've got the formula equaling the surface area.

So now what we need to try and do is figure out anything that we can substitute into the formula to help us work out the radius.

Well, we know that the sloped height, the slanted height, is 10 centimetres, so let's substitute that into the formula there on the left-hand side of the equation.

So another thing I can see on the left-hand side is that we've got two terms with the value of pi though, so we can factorise that value of pi out in that expression on the left hand side, so we'll do that.

The reason why I've done that is now I can divide both sides of the equation by pi.

What that does is remove pi from both sides of the equation.

So now I've got, what's left in the equation is a quadratic with just, as an unknown value there.

So I can now try and solve this quadratic equation.

So solve the quadratic equation.

I've got to make that equation equals zero.

I'm going to subtract 96 from both sides to make that quadratic equation equal to zero.

Now I can factorise that equation on the left-hand side, that factorises to r plus 16, in a bracket, and then the second bracket r subtract six.

Now I can solve that quadratic equation and I'll find both my solutions.

One solution will be r equals negative 16 or r equals six.

Now, think about the cone now, we can't have a negative radius, so we can dismiss that answer.

And we'll go with the radius equals six, and that's the solution to my problem there.

I've worked out the radius of the cone, of six, and that will give me a surface area of 96 pi.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer for the first question.

So the formula for the surface area of a cone is given to you there.

The problem is, however, you don't have the slant height, which you need to substitute into the formula.

However, you can work that out using Pythagoras's theorem.

I hope you got the correct answer there.

Here's another question you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

In this question, you have to work out the radius of Amir's marble.

You're given the surface area formula, and you're also given the surface area of Amir's marble.

So make an equation using those two, rearrange it and make r the subject, and that should give you the radius of Amir's marble.

Here's another question you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

If you didn't quite get the correct answer for this question, my first piece of advice for you here would be to draw each triangular face separately to figure out what the height of each triangle is, and you can use Pythagoras's theorem to help you with that.

And then you'll find that you have five faces to work out in order to find the surface area of this square-based pyramid.

That's all we have time for this lesson.

See you next time.