Question

given circles t and u below. find the area of the shaded region. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Determine radii of circles

From the diagram, the diameter of circle \( U \) is equal to the radius of circle \( T \). Let the diameter of circle \( U \) be \( d_U = 22 \), so the radius of circle \( U \), \( r_U=\frac{22}{2}=11 \). The radius of circle \( T \), \( r_T = 22 \) (since it's equal to the diameter of \( U \)).

Step2: Calculate area of circle \( T \)

The formula for the area of a circle is \( A=\pi r^2 \). For circle \( T \), \( A_T=\pi(22)^2 = 484\pi \).

Step3: Calculate area of circle \( U \)

For circle \( U \), \( A_U=\pi(11)^2=121\pi \).

Step4: Find area of shaded region

The shaded region is the area of circle \( T \) minus the area of circle \( U \). So, \( A_{shaded}=A_T - A_U=484\pi - 121\pi = 363\pi \).

Step5: Compute numerical value

Using \( \pi\approx3.1416 \), \( 363\pi\approx363\times3.1416\approx1140.4 \) (rounded to the nearest tenth).

Answer:

\( 1140.4 \) (or \( 363\pi \) if exact form is preferred, but the problem asks for a decimal rounded to the nearest tenth)