A shot put throwing area is a sector of an annulus with R=10m, r=2m, and angle theta=40 degrees. Calculate arc lengths EF and DG.

Alright Mercy — let's do this. The figure shows a shot put throwing area, which is a sector of an annulus. The common center is C. The radius of the larger circle is R = 10 m. The radius of the smaller circle is r = 2 m. The angle = ECF = 40^. We will use = 3.142. The formula for the arc length L of a sector with radius R and angle (in degrees) is: L = ()/(360^) × 2 R a) Calculate the arc length EF. Step 1: Identify the radius and angle for arc EF. Arc EF is part of the larger circle with radius R = 10 m and angle = 40^. Step 2: Apply the arc length formula and calculate. L_EF = (40^)/(360^) × 2 × 3.142 × 10 L_EF = (1)/(9) × 20 × 3.142 L_EF = (62.84)/(9) L_EF ≈ 6.9822 Rounding to three decimal places: L_EF ≈ 6.982 m The arc length EF is 6.982 m. b) Calculate the arc length DG. Step 1: Identify the radius and angle for arc DG. Arc DG is part of the smaller circle with radius r = 2 m and angle = 40^. Step 2: Apply the arc length formula and calculate. L_DG = (40^)/(360^) × 2 × 3.142 × 2 L_DG = (1)/(9) × 4 × 3.142 L_DG = (12.568)/(9) L_DG ≈ 1.3964 Rounding to three decimal places: L_DG ≈ 1.396 m The arc length DG is 1.396 m. c) Calculate the perimeter of the shaded region DEFG. Step 1: Identify the lengths of the straight segments DE and GF. The straight segments DE and GF are the difference between the radii of the two circles. DE = GF = R - r = 10 m - 2 m = 8 m Step 2: Sum all the lengths to find the perimeter. The perimeter P of the shaded region DEFG is the sum of arc length EF, arc length DG, and the two straight segments DE and GF. P = L_EF + L_DG + DE + GF P = 6.9822... + 1.3964... + 8 + 8 P = 8.3786... + 16 P = 24.3786... Rounding to three decimal places: P ≈ 24.379 m The perimeter of the shaded region DEFG is 24.379 m. Send me the next one 📸