I hate circle questions ca anyone help me ??? i am really stuck and i need to do these questions parts A&B?

Question

At winchester there is a large table know as the round table of King Arthur

The diameter of the table is 5.5 metres

a) a book claims tat 50 people sat around the table.

assume each person needs 45cm aound the circumference of the table
isit possible for 50 people to sit around the table?

show working to explain your answer???




B)))))))))
Assume people sitting around the table could reach only 1.5 m
diameter 2.75
calculate the area of the table that could be reached



plz can some one help me
i have dyslexia in maths and my teacher is strict

Answer 1

a)

If the diameter of the table is 5.5 metres this means that its circumference is
C = 5,5 x Pi = 17,27 metres.

each person needs 45cm around the circumference of the table

45 cm = 0.45 m

17,27 metres / 0.45 metres = 38, 39

This means that at most 38 people couls have sat around the table!!!


b)

they could reach only 1.5 m far towards the centre of the table. I guess here the RADIUS is 2.75 m, not the diameter!!!

This means, that nobody could reach a small circular area in the middle of the table. That circular area has radius 2.75m - 1.5m = 1.25m and its area is
A = Pi x r x r
A = Pi x 1.25m x 1.25m
A = 4,91 m^2

Now, the area of the whole table is
AREA = Pi x R x R = Pi x 2.75m x 2.75m = 23,76 m^2

So the area that could be reached is a ring (the table - the small circular area in the middle):
23,76 m^2 - 4,91 m^2 = 18,85 m^2


_______________________

If you have dyslexia, it is very important that you break your questions down into smaller bits and DRAW A SKETCH! It is much easier if you make a sketch. And make sure it is not too small!

Answer 2

Since most, people have answered a) correctly, let's move onto b).
Someone has stated that they assume that 2.75 is the radius and I must also go along with this person because this would give a diameter of 5.5m which the question originally states. Also if the diameter was 2.75m then the radius would be 1.375m which is less than the amount that the people can reach.

The area of the table that can be reached is the area of the whole table less the area that can't be reached. Which equals:-

pi R^2 - pi r^2 Where R is the radius of the table and r is the radius of the table which can't be reached. So we can simplify this to :- pi (R^2 - r^2).

Firstly we need to calculate r. This will be R - 1.5 which is
2.75 - 1.5 = 1.25. So the calculation is :- pi(2.75^2 - 1.25^2)
The part in brackets is in the form of (a^2 - b^2) which can be simplified to (a + b)(a - b) or, in our case :-
(2.75 + 1.25)(2.75 - 1.25) which is 4 x 1.5 = 6

So the answer is pi x 6 or approx 18.84 sq m.

Answer 3

here is the answer to the first part-
to figure the circumferance of a circle when you know the diameter you multiply pi and the diameter- thus 5.5 X 3.142 = 17.2810 meters- and and since 1 meter = 100 cm that would be 1,728.10 cm , and if 50 people sit at the table and each needs 45cm you do 50X45= 2,250cm therefore the answer is there in NOT enough room-

As for part B- if the diameter is 2.75 that makes the radias 1.37 and that means that they could reach the entire table and to figure the area of a circle you use pi R squared which then comes out to approx 5.90
I have encluded a link that is really good at giveing you the forumulas and how to solve them-
Happy Math
Betty

Answer 4

a. Table diameter is 5.5 meters and it is circular therefore the perimeter of the circle (that is the distance around it) is the diameter times pi

perimeter = 5.5 X 3.14 = 17.27 meters change the meters to centimeters by multiplying by 100. Therefore the perimeter is 1727 cm. if each person requires 45 cm space then the total number that can sit around the table is the perimeter divide by 45.

1727/45 = 38 people is the most that can sit around it.


b. the only solution to this part that I can think of off hand is by the use of calculus. I dont know if your are ready for that. There is surely a formula in a math book somewhere that will solve the problem.

Answer 5

For A))) you do Pi x 5.5 metres to find the circumference.Once you hav done that you divide the cirumference by 0.45 metres (45cm) and then if the answer is 50 or more then the answer to the question is yes 50 people can sit around the table but if it is less than 50 then the answer is no 50 people could not have sat around the table.

B))))) sorry dont know this one!!


hope it helps!!

Answer 6

a) Circumference of table = 5.5*100*Pi
Maximum number of people seated = 5.5*100*Pi/45 = 38
(5.5m has been multiplied by 100 convert to cm)
b) Accessible area = Table area - inaccessible area
= Pi (R^2 - (R-2r)^2)
Where R = Table radius; r = persons reach. Your figures must be incorrect because if people can reach 1.5m, the centre and hence the entire area of a 2.75m diameter table can be accessed by everyone.

If part (b) refers to the area accessible by a single person sitting at a 2.75m diameter table, you have jumped from trivial geometry to an A-Level question, which seems unlikely.

Answer 7

a) firstly we need to work out the circumference of the circle which is pi X diameter = 3.142*5.5 = 17.278759594743m
multiply by 100 to convert it to centimetres = 1727.8759594743862811544538608037cm

now we need to work out the 'circumference' of the people sitting round the table 50*45 = 2250cm. this is clearly more than the circumference of the table so no 50 people couldn't. in fact only 38 could.

as for b) i'm not sure

Answer 8

a) Circumference of circle = 2 pi r or pi*d
so 5.5 *3.142 = 17.28m

No of people that can sit at the table = 17.28/0.45m approx 38
So the answer is no.
b) I did not understand your second question what is 2.75 diameter.

If that is the diameter of the table then all of the table could be
reached. 2*1.5 = 3m diameter.

If we are talking about King Arther's table then
Then diameter of circle not reached = 5.5-(2*1.5) = 2.5m
Area of table = pi r^2 = 3.142*2.75*2.75 = 23.761m^2
Area of table not reached = pi*1.25*1.25 = 4.91m^2
Area of Table reached = area of table - area of table not reached

=23.761-4.91 = 18.851m^2

Answer 9

Diameter = 5.5m
Radius = 2.25
Pi= 3.141

2.25 * 3.141=7.06
50 X 0.45 = 22.5m squared

Draw a circle, scale it to 5.5 cm, use it as a pie chart and devide it into 50. Draw 50 smaller circles in it where each person is sitting, scale them to 2.75 cm in diameter.
2pi r to work out the circumfrence.
= 14.13. I think you may have the wrong table.

Answer 10

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