This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the dimensions of the running track. The running track consists of a rectangular middle section and two semi-circular ends. The length of the straight sides (length of the rectangle) is L = 110 m. The diameter of each semi-circle is D = 70 m. The radius of each semi-circle is r = (D)/(2) = (70)/(2) = 35 m. The width of the rectangular section is equal to the diameter of the semi-circles, W = 70 m. Use = (22)/(7). Step 2: Calculate the distance round the field (perimeter). The distance round the field is the sum of the lengths of the two straight sides and the circumference of the two semi-circular ends. The two semi-circular ends together form a full circle. Perimeter P = 2 × L + Circumference of a full circle The circumference of a full circle is D. P = 2L + D Substitute the given values: P = 2(110 m) + ((22)/(7))(70 m) P = 220 m + (22 × 10) m P = 220 m + 220 m P = 440 m The distance round the field is 440 m. Step 3: Calculate the area of the field. The area of the field is the sum of the area of the rectangular middle section and the area of the two semi-circular ends. The two semi-circular ends together form a full circle. Area A = Area of rectangle + Area of a full circle The area of the rectangle is L × W. The area of a full circle is r^2. A = (L × W) + r^2 Substitute the given values: A = (110 m × 70 m) + ((22)/(7))(35 m)^2 A = 7700 m^2 + ((22)/(7))(1225 m^2) A = 7700 m^2 + (22 × 175) m^2 A = 7700 m^2 + 3850 m^2 A = 11550 m^2 The area of the field is 11550 m^2. That's 2 down. 3 left today — send the next one.