Surface area and sector area GCSE

First attachment: at first glance you appear to have missed out the sides that you can't see :tongue:

Reply 2

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?
Add those on and you have your answer.

2.

I assume you know the arc length =

r\theta

.

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

\theta

.

We also know that the Area of a sector is

\frac{1}{2}r^{2}\theta

.

With the information found out, we can plug our numbers into the formula giving us the area of the sector.

(edited 11 years ago)

Reply 3

OP

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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Reply 4

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.

Posted from TSR Mobile

Check over face 2, that has been mis-calculated.

Reply 5

OP

ImageUploadedByStudent Room1364341050.310782.jpg102.9KB

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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ImageUploadedByStudent Room1364341088.859529.jpg93.2KB

Reply 6

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 :smile:

.

Reply 7

1.

You have forgotten face 7!

2.

Ok, ultimately we want the area of the sector (

A = \frac{1}{2}r^{2} \theta

).

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

A = \frac{1}{2}(10)^{2}\theta = 50\theta

So we now need to find

\theta

.

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

L = r \theta

.

If we plug in what we have:

15 = 10 \theta

Can you work from here to find

\theta

and then the area?

Reply 8

Robbie242

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.

Posted from TSR Mobile

L=r\theta

Arc length is L, plug in rearrange for theta and plug that into the area of a sector formula

Reply 9

OP

Alright so I did the 7th side and got 110cm squared, thanks a lot for the help. :biggrin:

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! :tongue:

Is theta = 9 so 10 x 9 = 90?

(edited 11 years ago)

Reply 10

you don't need to know the angle from those equations, just your simple circle ones, scroll up a little :smile:

Reply 11

OP

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 :smile:

.

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

Reply 12

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

Reply 13

OP

Original post by Season One

Do 15/(3.14x20) not 15/20

I'm pretty sure I've done this wrong again. :tongue:

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

Reply 14

Original post by yellowcopter

I'm pretty sure I've done this wrong again. :tongue:

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 :smile:

(edited 11 years ago)

Reply 15

OP

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 :smile:

So the answer is 0.7499? This is so confusing. :tongue:

I should really get myself a revision guide.

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Reply 16

Original post by yellowcopter

So the answer is 0.7499? This is so confusing. :tongue:

I should really get myself a revision guide.

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No.

The area of a sector is

\frac{1}{2}r^{2}\theta

We have the radius

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

r\theta

:

So with this information we can form an equation to find

\theta

:

Which is what I had shown you before:

15 = 10\theta

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?

(edited 11 years ago)

Reply 17