The radius of the outer circle is half of the outer diameter, which is $1.7$ m. So, the outer radius $R = \frac{1.7}{2} = 0.85$ m.
The diameter of the inner circle is the outer diameter minus twice the thickness. The outer diameter is $1.7$ m, and the thickness is $1.4$ m. The inner diameter is $1.7 - 1.4*2 = -1.1$ m.
Radius of inner circle is $\frac{-1.1}{2} = -0.55$ m. Since the radius cannot be negative, we take the radius to be $0.55$ m. The thickness is given as 1.4 m whereas the total diameter is 1.7m, so the thickness must be less than $\frac{1.7}{2}$ m.
Since the outer diameter is 1.7 m, and the thickness of the ring is 1.4 m, the inner diameter is $1.7 - 2(1.4) = 1.7 - 2.8 = -1.1$ m, but this is physically impossible. It appears there is an error in the problem statement.
Alternative interpretation: The thickness of 1.4 m could be referring to the width of the colored ring, not the entire ring to the center.
The diameter of the inner circle in this case can be found as: $1.7 - 1.4 = 0.3$. Therefore, the inner radius $r$ is $\frac{0.3}{2}=0.15$ m.
The colored area is the difference between the area of the outer circle and the area of the inner circle. The formula for the area of a circle is $A = \pi r^2$, where $r$ is the radius.
If the inner radius is $0.55$ m:
Area $= \pi R^2 - \pi r^2 = \pi(0.85^2) - \pi(0.55^2) = \pi(0.7225 - 0.3025) = 0.42\pi \approx 1.32$
If the thickness of the colored region is $1.4$ m:
Area $= \pi R^2 - \pi r^2 = \pi(0.85^2 - 0.15^2) = \pi(0.7225 - 0.0225) = \pi(0.7) = 0.7\pi \approx 2.20$
Answered
