Answer:
33%
Step-by-step explanation:
The area of a circle is [tex]\pi r^{2}[/tex] , where r is the radius. In this case, the area of the second largest circle is [tex]\pi (3+4)^{2}[/tex] (because the radius is 3 + 4 = 7) = 49[tex]\pi[/tex].
The area of the smallest circle is [tex]\pi 4^{2}[/tex] = 16[tex]\pi[/tex].
Now, the area of the shaded region is just the smallest circle's area subtracted from the second-largest circle's area:
49[tex]\pi[/tex] - 16[tex]\pi[/tex] = 33[tex]\pi[/tex]
To find the percentage of the logo that is shaded, we need to find the total area, which is just the area of the largest circle: [tex]\pi *(4 + 3 + 3)^{2} = \pi *10^{2} = 100\pi[/tex]
Now, we just divide 33[tex]\pi[/tex] by 100[tex]\pi[/tex] to get:
33[tex]\pi[/tex]/100[tex]\pi[/tex] = 33/100 = 33%, which is our answer.
