# Diameter

• Apr 30th 2010, 01:34 PM
molly
Diameter
I've got a maths exam next week and i need to know how to work this question out for my revision so please could u show me:

The diameter of a table is 5.5 metres. A book claims that 50 people sat around the table. Assume each person needs 45 cm around th circumference of the table. is it possible for 50 people to sit around the table? show your working to explain your answer.
• Apr 30th 2010, 01:42 PM
shenanigans87
First find the circumference.

$\displaystyle \text{circumference}=2\pi\;r$

The diameter of the table is twice the radius.

$\displaystyle 2r=5.5 \;\text{meters}$ so $\displaystyle r=2.75 \;\text{meters}$

and

$\displaystyle \text{circumference}=2\pi*r=2\pi*2.75=17.28\;\text {meters}$

And we know that $\displaystyle 17.28\;\text{meters}*100=1728\;\text{cm}$

You need to fit 50 people with 45 cm per person. That's $\displaystyle 50*45=2250\;\text{cm}$

Since $\displaystyle 2250\geq 1728$, they will not fit, because you need at least 2250 cm and you only have 1728.