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: Calculate the area of the pitch (1.1.1) The pitch is a rectangle with a length of 23 m and a width of 4 m. A_pitch = length × width A_pitch = 23 m × 4 m A_pitch = 92 m^2 The area of the pitch is 92.00 m^2. Step 2: Calculate the area of the oval (1.1.2) The oval is a stadium shape, composed of a rectangular section and two semi-circular ends. The length of the rectangular section is 20 m. The radius of the semi-circular ends is r = 64 m. The width of the rectangular section is equal to the diameter of the semi-circles, which is 2r = 2 × 64 m = 128 m. Area of the rectangular part of the oval: A_rect\_oval = 20 m × 128 m = 2560 m^2 Area of the two semi-circular ends (which form one full circle): A_circle = r^2 A_circle = × (64 m)^2 A_circle = × 4096 m^2 ≈ 12867.9635 m^2 Total area of the oval: A_oval = A_rect\_oval + A_circle A_oval = 2560 m^2 + 12867.9635 m^2 A_oval = 15427.9635 m^2 Rounding to two decimal places: The area of the oval is 15427.96 m^2. Step 3: Calculate the area of the grass only (1.1.3) The area of the grass is the area of the oval minus the area of the pitch. A_grass = A_oval - A_pitch A_grass = 15427.9635 m^2 - 92 m^2 A_grass = 15335.9635 m^2 Rounding to two decimal places: The area of the grass only is 15335.96 m^2. Step 4: Calculate the average number of seats in one block (1.2.1) The stadium has a capacity of 28000 seats arranged in 8 blocks. Seats per block = Total capacityNumber of blocks Seats per block = 28000 seats8 blocks Seats per block = 3500 seats/block On average, there are 3500 seats in one block. Step 5: Verify the caretaker's claim about the number of rows (1.2.2) Each row of seats needs a height of 700 mm. The stadium height is 30 m. The caretaker claims there are 43 rows. First, convert the height per row to meters: 700 mm = 0.7 m Calculate the total height required for 43 rows: Total height for 43 rows = 43 × 0.7 m Total height for 43 rows = 30.1 m Compare this to the stadium height: The calculated height required for 43 rows is 30.1 m, which is greater than the stadium's height of 30 m. Therefore, the caretaker's claim is Incorrect. Send me the next one 📸