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A round cake with diameter 20cm is shared equally between 6 people. Find the perimeter and the area of the top of each piece. Leave pi in your answer.

A 1.5m long pendulum travels from one extreme of its swing to the other in half a second. In this time, the bob at the bottom of the pendulum travels pi/10m. Find out how long it takes for the pendulum to sweep out the equivalent of a complete circle. I've tried working out the angle using the sector length formula but I don't know what to do next or if my sector angle is even correct (I got 0.05 radians)

Thanks
2. (Original post by HumiT)

A round cake with diameter 20cm is shared equally between 6 people. Find the perimeter and the area of the top of each piece. Leave pi in your answer.
What have you done here as it seems very straight forward

A 1.5m long pendulum travels from one extreme of its swing to the other in half a second. In this time, the bob at the bottom of the pendulum travels pi/10m. Find out how long it takes for the pendulum to sweep out the equivalent of a complete circle. I've tried working out the angle using the sector length formula but I don't know what to do next or if my sector angle is even correct (I got 0.05 radians)
You do not need the angle
You know the distance travelled in 0.5 sec
You know the distance to be travelled ... again pretty straight forward
3. (Original post by TenOfThem)
What have you done here as it seems very straight forward
Nothing

(Original post by TenOfThem)
You do not need the angle
You know the distance travelled in 0.5 sec
You know the distance to be travelled ... again pretty straight forward
Yes but I can't get the right answer.
4. (Original post by HumiT)
Nothing
Do you know the rules for arc length and sector area

I am struggling to find the problem with this question
5. (Original post by HumiT)
Yes but I can't get the right answer.
What answer do you get .. can you show some working
6. (Original post by HumiT)
A round cake with diameter 20cm is shared equally between 6 people. Find the perimeter and the area of the top of each piece. Leave pi in your answer.
First, find the area of the whole cake (the top of the cake that is)
Area of a circle = pi * (radius)^2
The radius in this case is 10cm
So the total area would be = 100(pi)
So the area of each piece would be the total area divided by six, giving:
50pi/3 cm^2

Now you look at the perimeter of each piece.
You know the perimeter of the circle is 2*pi*(radius)
Which gives you total perimeter to be 20pi
But when you slice it into 6 pieces, you have to consider the lengths of the two other sides of the slice. But the length of each of those two sides is the radius (10cm)

So the perimeter of each piece would be:
(20pi / 6) + 10 + 10
Giving: 20 + 5pi/3

Hope I helped
7. (Original post by TenOfThem)
Do you know the rules for arc length and sector area

I am struggling to find the problem with this question
area = 1/2r^2theta
arc length = r x theta

(Original post by TenOfThem)
What answer do you get .. can you show some working
Well I don't have much working, all I did was minus pi/10m from 1.5m and then tried multiplying that by 0.5 and obviously that's not right
8. (Original post by HumiT)
area = 1/2r^2theta
arc length = r x theta
Well you know r and theta so what is the problem

Well I don't have much working, all I did was minus pi/10m from 1.5m and then tried multiplying that by 0.5 and obviously that's not right
I do not think you have understood what was asked tbh

It travels pi/10 in 0.5 sec
You want it to travel the length of the circumference = 2pi r
You know r
9. (Original post by rohan95)
First, find the area of the whole cake (the top of the cake that is)
Area of a circle = pi * (radius)^2
The radius in this case is 10cm
So the total area would be = 100(pi)
So the area of each piece would be the total area divided by six, giving:
50pi/3 cm^2

Now you look at the perimeter of each piece.
You know the perimeter of the circle is 2*pi*(radius)
Which gives you total perimeter to be 20pi
But when you slice it into 6 pieces, you have to consider the lengths of the two other sides of the slice. But the length of each of those two sides is the radius (10cm)

So the perimeter of each piece would be:
(20pi / 6) + 10 + 10
Giving: 20 + 5pi/3

Hope I helped
Ahh right..thanks

(Original post by TenOfThem)
Well you know r and theta so what is the problem

I do not think you have understood what was asked tbh

It travels pi/10 in 0.5 sec
You want it to travel the length of the circumference = 2pi r
You know r
What is theta in the first question

And then what do I do after that?
10. (Original post by HumiT)
What is theta in the first question
I am guessing that you do know the angle for the full circle and that you can divide that amongst the 6 pieces
11. (Original post by TenOfThem)
I am guessing that you do know the angle for the full circle and that you can divide that amongst the 6 pieces
What do I need to do for the second question?
12. (Original post by HumiT)
What do I need to do for the second question?
You know the distance traveled in 0.5 seconds, so you can work out speed. You can find the distance needed to be traveled (circumference = 2rpi)
so speed = distance/time
13. (Original post by HumiT)
What do I need to do for the second question?

pi/10 takes 0.5 sec

you need the circumference
14. (Original post by Tomupcraft)
You know the distance traveled in 0.5 seconds, so you can work out speed. You can find the distance needed to be traveled (circumference = 2rpi)
so speed = distance/time
thanks

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