Applications of trig

Hi, could someone please help me on these questions; (all angles are measured in radians)

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 :smile:

Reply 1

TenOfThem

Original post by HumiT

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

Reply 2

HumiT

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.

Reply 3

TenOfThem

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

Reply 4

TenOfThem

Original post by HumiT

Yes but I can't get the right answer.

What answer do you get .. can you show some working

Reply 5

rohan95

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 :smile:

Reply 6

HumiT

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 :colondollar:

Reply 7

TenOfThem

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 :colondollar:

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

Reply 8

HumiT

Original post by rohan95

Ahh right..thanks :smile:

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 :confused:

And then what do I do after that?

Reply 9

TenOfThem

Original post by HumiT

What is theta in the first question :confused:

I am guessing that you do know the angle for the full circle and that you can divide that amongst the 6 pieces

Reply 10

HumiT

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?

Reply 11

Tomupcraft

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

Reply 12

TenOfThem

Original post by HumiT

What do I need to do for the second question?

I told you already

pi/10 takes 0.5 sec

you need the circumference

Reply 13

HumiT

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