Math Is Fun Forum

Joseph

Guest

6th grade math

Which has the greater area:
a circle with circumference of 40.5 feet or
acircle with radius 80 in?
Explain.

                                                                    Can you make it simple with the explaination?

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: 6th grade math

Find the areas of the two circles and compare them?

You must understand that your dealing with different measurements. Inches and Ft. Convert to one or the other.

40.5 ft = 486 inches.

Thats the diameter of the circle so the radius is half of that, 243.

Area of a circle is equal to: PI times its radius squared.

So the area of the first circle with radius 243in is 185,413.86 inches squared.

The area of the the second circle with radius 80in is 20,096 inches squared.

Clearly the first one has a greater area.

Last edited by LuisRodg (2008-03-13 23:58:17)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 6th grade math

The 80 inch radius is 160 inch diameter.

The 40.5 foot circular distance divided by a bit more than 3
is the secret to getting the diameter.
The secret 3 number is a tiny bit more than 3.
40.5 / 3.141592653589793238462643383279 = 12.8915504 foot diameter.

We know one circle in feet and the other in inches.
40.5 circle:
  40.5 feet around --> 12.8915504 feet across --> tmz 12 ---> 154.698605 inches across
80 circle:
  80 inches half across --> 160 inches across

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igloo myrtilles fourmis

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: 6th grade math

John E. Franklin got it right.

I completely missed the part about it being the circumference and assumed it was the diameter. My bad.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: 6th grade math

Odd.  I did the same thing Luis.  That's really... odd.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."