Question

The surface inside the circles will be painted green. The surface outside the circles will be painted white. What is the ratio of green paint to white paint?
A. π : (4 - π)
B. (4 - π) : π
C. π : (π - 4)
D. π^2 : (4 - π^2)

Answer 1

Answer:

The ratio of green paint to white paint is A. $\pi:(4-\pi)$

Step-by-step explanation:

To find the ratio of green paint to white paint we need to divide the surface that will be painted green by the surface that will be painted white.

In the graph we can see 4 equal circles. Let be ''R'' the radius of the circles.

We can also see a square. The side of the square is 4R (because the length of the side is 4 times the radius of any circle).

The surface of a circle which radius is ''R'' is equal to :

$\pi .R^{2}$

The surface inside this 4 circles is equal to :

$4.\pi .R^{2}$

The surface $4.\pi .R^{2}$ will be painted green.

The surface outside the circles is equal to $4.\pi .R^{2}$ subtracted to the area of the square.

The area of the square is :

$(4R)^{2}=16R^{2}$ ⇒

$16R^{2}-4.\pi.R^{2}$ is the surface that will be painted white.

If we make the division between the surfaces :

$\frac{GreenSurface}{WhiteSurface}$ ⇒

$\frac{4.\pi .R^{2}}{16R^{2}-4.\pi .R^{2}}$

$\frac{(4R^{2}).\pi}{(4R^{2}).(4-\pi)}=\frac{\pi}{4-\pi}$

We find that the ratio of green paint to white paint is $\pi:(4-\pi)$

Answer 2

B / a right .?????/////.