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# Surface area and sector area GCSE watch

1. On the first attachment I've done the question but my friend has told me the answer is 110cm squared as his teacher told him, however I got 67, what am I doing wrong?

And for the second attachment how do I do this question? Do I find the area of the whole circle and divide it by 4? I was going to but I realised it was at an angle and not quarter circle. Thanks!

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Attached Images

2. First attachment: at first glance you appear to have missed out the sides that you can't see
3. 1.

Imagine standing under the prism, what face would you seen then?
Also imagine standing to the left of the object, what face do you see then?

2.

I assume you know the arc length = .

So we know what the arc length is, we know what the radius is, we can then use that to find .

We also know that the Area of a sector is .

With the information found out, we can plug our numbers into the formula giving us the area of the sector.
4. Thanks a lot guys, so for the first question I would do the left side which is 3 x 6 = 18 and then the bottom 5 x 6 = 30; add them up to get 48 and then do 67 + 48 which is 115cm squared? Is that correct or is there something wrong?

As for the other question I'm starting it now, thanks for explaining the formula.

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5. (Original post by yellowcopter)
Thanks a lot guys, so for the first question I would do the left side which is 3 x 6 = 18 and then the bottom 5 x 6 = 30; add them up to get 48 and then do 67 + 48 which is 115cm squared? Is that correct or is there something wrong?

As for the other question I'm starting it now, thanks for explaining the formula.

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Check over face 2, that has been mis-calculated.
6. (Original post by Joshmeid)
Check over face 2, that has been mis-calculated.
I got 103cm squared in this end, is there anything I've done wrong?

I also attached my answer to the other question but I haven't got a clue when it comes to sin cos tan.

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Attached Images

7. Well you can work out the angle by using your simple circle equations. As you know the radius you can work out the circumference. Circumference= pi x diameter. Once you know this value, do 15/answer to work out what percentage of the circle it is. Then work out the area doing Pi x radius ^2. Then times this answer by whatever the (15/pi x diameter) is .
8. 1.

You have forgotten face 7!

2.

Ok, ultimately we want the area of the sector ( ).

Now if we plug in what we have available from the question it leaves us with:

So we now need to find .

Well seeing as we're given the arc length and radius we can use the handy formula for arc length: .

If we plug in what we have:

Can you work from here to find and then the area?
9. (Original post by yellowcopter)
I got 103cm squared in this end, is there anything I've done wrong?

I also attached my answer to the other question but I haven't got a clue when it comes to sin cos tan.

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Arc length is L, plug in rearrange for theta and plug that into the area of a sector formula
10. Alright so I did the 7th side and got 110cm squared, thanks a lot for the help.

As for the second question I don't know how to find out 10 theta, I've never learnt it because I'm only a C grade but I'm attempting these questions to try and raise my game. I understood everything you said excluding the theta thingy, heck I even did cos when that's a circle and not a triangle!

Is theta = 9 so 10 x 9 = 90?
11. you don't need to know the angle from those equations, just your simple circle ones, scroll up a little
12. (Original post by Season One)
Well you can work out the angle by using your simple circle equations. As you know the radius you can work out the circumference. Circumference= pi x diameter. Once you know this value, do 15/answer to work out what percentage of the circle it is. Then work out the area doing Pi x radius ^2. Then times this answer by whatever the (15/pi x diameter) is .
I'm still really confused, is this correct?

3.14 x 20
15 / 20 = 0.75

3.14 x 10 squared = 314
314 x 0.75 = 235.5
13. (Original post by yellowcopter)
I'm still really confused, is this correct?

3.14 x 20
15 / 20 = 0.75

3.14 x 10 squared = 314
314 x 0.75 = 235.5

Do 15/(3.14x20) not 15/20
14. (Original post by Season One)
Do 15/(3.14x20) not 15/20
I'm pretty sure I've done this wrong again.

15 / (3.14 x 20) = 0.23885350318
15 / (3.14 x 10
^2) = 0.04777070063
0.23885350318 x 0.04777070063 = 0.01141019919
15. (Original post by yellowcopter)
I'm pretty sure I've done this wrong again.

15 / (3.14 x 20) = 0.23885350318
15 / (3.14 x 10
^2) = 0.04777070063
0.23885350318 x 0.04777070063 = 0.01141019919

15/(3.14x20)= 0.23885350318 this stage is right.
Now do pi x 10^2 which is basically 100pi.
then do 100pi x 0.23885350318 .... = answer

16. (Original post by Season One)
15/(3.14x20)= 0.23885350318 this stage is right.
Now do pi x 10^2 which is basically 100pi.
then do 100pi x 0.23885350318 .... = answer
So the answer is 0.7499? This is so confusing.

I should really get myself a revision guide.

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17. (Original post by yellowcopter)
So the answer is 0.7499? This is so confusing.

I should really get myself a revision guide.

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No.

The area of a sector is

We want to know the size of the angle of the sector as we have everything else to calculate the area.

We know that the arc length is equal to :

So with this information we can form an equation to find :

Which is what I had shown you before:

Now can you rearrange this equation to find theta?

Once you have theta can you substitute that back into the equation for the area of a sector and then find your area?
18. (Original post by Joshmeid)
No.The area of a sector is We have the radiusWe want to know the size of the angle of the sector as we have everything else to calculate the area.We know that the arc length is equal to o with this information we can form an equation to find :Which is what I had shown you before:Now can you rearrange this equation to find theta?Once you have theta can you substitute that back into the equation for the area of a sector and then find your area?
I don't think you do Radians at GCSE
19. Basically:

Arc Length = R*Theta
Area of Sector = R^2*1/2*Theta
Area of Triangle = R^2*1/2*SinTheta

You need to find theta, in radians btw.

You know arc length and radius so:

15 = 10*Theta

Area of Sector = 10^2 * 1/2 * 1.5

50*(1.5)

= 75cm^2

Do you get it now?
20. I thought the formula to find the area of a sector was theta / 360 x pi x r^2?

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