Question

Please help its not working

Answer 1

Answer:

$33\%$

Step-by-step explanation:

To work out the percentage of the circle shaded blue, we first must work out the area of the whole circle.

Area of the whole circle = $\pi r^2$

$r=4+3+3\\\pi * (4+3+3)^2=\pi*10^2=100\pi$

Now we need to work out the area of the blue 2d torus, by finding out the area of the blue circle, then subtracting the area of the innermost white circle.

Blue shaded area = $\pi(r_{0}{^2}-r_{1}{^2})$

$r_0=4+3\\r_1 = 4\\\pi ((4+3)^2-(4)^2)= \pi (7^2-4^2)=33 \pi$

Now we have the total areas of each, we can work out the fraction of blue to non blue by dividing the blue area by the total area, and then working out the percentage by multiplying by 100.

$\frac{33\pi}{100\pi}*100=\frac{33\pi}{\pi}=33\%$