Dorcus wants to build a fish pond with semicircular ends. She takes 28 paces for each 20 meters, and paces out the area. The total length for the pond is 283 paces and the height is 14 paces. According to the information given answer the following:
1. Determine the pace length
2. Convert the distance in paces to meters
3. Find the area needed for the fish pond. Give your answers in square meters.
1. The pace length can be calculated by dividing the total distance in paces by the total distance in meters:
Pace length = Total distance in paces / Total distance in meters
Pace length = 283 / 20
Pace length = 14.15 paces
2. To convert the distance from paces to meters, we can use the pace length calculated in the previous step:
Total distance in meters = Total distance in paces x Pace length
Total distance in meters = 283 x 14.15
Total distance in meters = 4000.45 meters
3. The area of the fish pond can be calculated by:
Area = 0.5 x (Length + 2r) x Height
Area = 0.5 x (4000.45 + 2(14.15)) x 14
Area = 0.5 x (4000.45 + 28.3) x 14
Area = 0.5 x 4028.75 x 14
Area = 28201.25 square meters
Therefore, the pace length is 14.15 paces, the distance in meters is 4000.45 meters, and the area needed for the fish pond is 28201.25 square meters.
The answer for 1 is 0.714m. The answer for 2 is 100.71m and 170m. The answer for 3 is 14944m²
Apologies for the incorrect calculation. Let's correct the answers:
1. Pace length = Total distance in meters / Total distance in paces
Pace length = 20 / 28
Pace length = 0.714 meters
2. Convert the distance in paces to meters:
Total distance in meters = Total distance in paces x Pace length
Total distance in meters = 283 x 0.714
Total distance in meters = 201.942 meters
3. Calculate the area of the fish pond:
Area = 0.5 x (Length + 2r) x Height
Area = 0.5 x (201.942 + 2*14.15) x 14
Area = 0.5 x (201.942 + 28.3) x 14
Area = 0.5 x 230.242 x 14
Area = 1611.694 square meters
Therefore, the pace length is 0.714 meters, the distance in meters is 201.942 meters, and the area needed for the fish pond is 1611.694 square meters.