Now let’s have a look at this diagram that we have here of what remains of a birthday
cake or the remains of a circle here of a full this circle thing.
So, what we have here in yellow is the shaded area that we are required to find the area,
that’s the outcome, that’s our objective.
Now the yellow area can be found except someone took out of this white area so a bit of this
cake is disappeared.
So how do we work out what’s left in terms of area?
Well doesn’t it make sense that all we need to do is know how to work out the full area
of a circle – pi r squared and then multiply that by the fraction of what is left, now
we take a closer look now on how we do this.
So first of all we have to write down the area of a full circle, now many of you already
know that – many of you know that and see that, yup – for the circle it’s pi r squared.
Where R is the Radius and here our radius happens to be 9 centimeters, now let’s have
a closer look at this, now if the full circle is pi r squared, what is the part of this
circle – now mind you, the good news is we have been given what the angle and it’s
270 degrees.
Now that’s 270 degrees, hmm – how can we work this out?
Well, it’s 270 degrees of what?
What is the total?
The total is 360 so another words the area of this yellow piece of cake here or yellow
disk is 270 degrees of the original 360 isn’t that the fraction?
So let’s write that down so 270 degrees is what we have here, right, that is the yellow
part of what was originally the whole thing and that was 360, that is the angle for the
whole area here – there’s our fraction – 270 over 360 then all we need to do is
multiplied by the area of a full circle which is pi r squared, let’s write that down – ok
this is our formula that is the area of a full circle now let’s simplify the 270 degrees
over the 360 degrees, well if we do in the calculating it is simplifies down into a very
basic fraction and that is 3 quarters and its actually looks like 3 quarters and it
is actually looks like 3 quarters and we can actually see that already.
Times pi r squared, let’s put the numbers in there, now we know what R is – it’s
given here as 9 centimeters here so maybe we can substitute that in there – so it’s
going to be 3 quarters – let’s write down here – times pi, times as I said before
– 9 centimeters is the radius and let’s square that because it is pi r squared – r
squared – so if we put that in the calculator we have 3 quarters times pi times 9 squared
and 9 squared is 81 – our grand total for the total area, all of this yellow part, the
yellow part of this 3 quarters circle is – in total 190.85 centimeters.
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