Question

a discus circle is shown to the right. it has a diameter of 98.5 inches that includes a 3 - inch - wide painted circle.
a. find the area of the discus circle.
b. find the area of the inner circle without the painted ring.
c. use parts a and b to find the area of the painted ring.

a. find the area of the discus circle
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Find radius of discus circle

The diameter is 98.5 inches, so radius $r_1 = \frac{98.5}{2} = 49.25$ inches.

Step2: Calculate area of discus circle

Use area formula $A = \pi r^2$.
$A_1 = \pi (49.25)^2 \approx 3.1416 \times 2425.5625 \approx 7617.13$

Step3: Find radius of inner circle

The ring is 3 inches wide, so inner radius $r_2 = 49.25 - 3 = 46.25$ inches.

Step4: Calculate area of inner circle

$A_2 = \pi (46.25)^2 \approx 3.1416 \times 2139.0625 \approx 6939.79$

Step5: Calculate area of painted ring

Subtract inner area from total area.
$A_{\text{ring}} = A_1 - A_2 = 7617.13 - 6939.79 = 677.34$

Answer:

a. 7617.13 square inches
b. 6939.79 square inches
c. 677.34 square inches