do ten circles with a diameter of 10 equal the area of a circle with a diameter of 100???

Answer 1

no because area of a circle is pi(r^2)

d=10
r=5

pi(25)*10=250pi

d=100
r=50
pi(50^2)=2500pi

Answer 2

Area of circle = pi r^2
Circle with diameter of 100
A = pi (50)^2 or 2500pi

10 circles with diameter of 10
A = pi 5^2 or 25pi, then multiply by 10 for the ten circles
250pi

So, no they do not, reason is because of squaring the radius

Answer 3

area of 10 circles with diameter of 10 is: 785.398
are of circle with diameter of 100 is: 7853.98
so the answer is no

Answer 4

Take any shape and increase by a factor of 10, then the area will increase 100 times. More generally, if the shape is increased by a factor of n, the area increases n^2 times.

In other words, you'd need 100 circles, not 10.

By the way, I think the folks calculating the areas of the circles are working too hard. :)

Answer 5

no not exactly 10 circles with the diameter LINED up would be 100 but not in a circle

Answer 6

I'm assuming you're asking if their areas are equal:

Circles c1, c2, ... c10 have diameter d = 10, and therefore

area of c1, c2, ... = pi*r^2 = pi * 25 = 3.14 * 25 = 78.5

Total Area of c1, .. c10 = 78.5 x 10 = 785


Area of a circle S with D = 100 =

area of S = pi*r^2 = pi * 50*50 = 7850


7850 != 785 , so NO - THEY ARE NOT EQUAL

Answer 7

Well let's try this out:

the area of a circle is (pi)r^2 so:

10 * (pi)(5)^2
10 * 25(pi)
250(pi)

(pi)(50)^2
2500(pi)

as you can see the 10 circles don't have the same area as the other sole circle.

Answer 8

A = pi r^2

D = 10
A = pi 5^2
10 circles: area is 10(25pi) = 250pi.

D= 100
A = pi(50)^2
= 2500pi.
Conclusion: No.

Answer 9

Ah! I knew it! Size DOES matter!