Math homework question?

Question

It's about a circle, and if you have an answer plaese explain it!

It will take the area of 16 circles of radius 24 to equal the area of one circle of radius________.

I know that it PROBABLY starts with a 1, and I KNOW that the number has three didgets.

Answer 1

area1 = area2
16 (pi) (24) (24) = (pi) sqr(radius)
radius = sqrt(9216)
radius = 96

Answer 2

Suppose a circle of radius x has the required area.
Then pi*x^2 = 16*pi*24^2.
Dividing by pi:
x^2 = 16 * 24^2
Taking the square root:
x = 4 * 24 = 96.

Answer 3

The answer is 96.
You get an area for each circle of 576 pi. There are a total of 16 of these, so the total area is 9216 pi. The area of a circle is pi times radius squared so the equation looks like this:
r(squared) times pi = 9216 pi
divide both sides by pi and you get:
r(squared) = 9216
take the square root of each side and you get:
96

The simpler answer is that you take the square root of 16 and get 4 four times 24 is 96.

Answer 4

Area of a circle is: pi * radius-squared.

That first circle, let's call it radius-1.

You want the area of one circle to equal the area of a 16 circles with a radius 24.

Therefore:
(pi) (R1)^2 = (16) (pi) (24)^2

I'll leave it to you to solve accordingly.
Good Luck!

Answer 5

Area = pi x radius x radius

so if you have 16 circles with radius 24, the area is given by area A=16.pi.24^2

The big circle has this area A which equals pi.R^2

R^2 = 16.24^2
R = SQRT(9216) = SQRT(4.4.24.24)
R = 96

Answer 6

Please do your homework by yourself or you will not learn any thing(try again and again)and if you fail ask .