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
Here are the calculations: 1.2.3 Determine whether the fabric roll width is sufficient to cut the tablecloth in one piece. Step 1: Identify the required dimension for the tablecloth. The new diameter of the tablecloth (calculated in 1.2.1) is 2.0 m. To cut a circular tablecloth of this size in one piece, the fabric roll width must be at least 2.0 m. Step 2: State the assumed fabric roll width. The fabric roll width is not provided in the problem statement. For the purpose of this calculation, we will assume a common fabric roll width of 1.5 m. Step 3: Compare the required width with the assumed roll width. Required width = 2.0 m Assumed roll width = 1.5 m Step 4: Conclude whether the roll width is sufficient. Since 1.5 m < 2.0 m, the assumed fabric roll width of 1.5 m is not sufficient to cut the tablecloth in one piece. The answer is No, the fabric roll width is not sufficient (assuming a 1.5 m roll width). 1.2.4 Calculate the minimum length of fabric required from the roll to cut ONE tablecloth. Step 1: Identify the minimum length needed. To cut a circular tablecloth of diameter 2.0 m from a roll, the minimum length of fabric required from the roll is equal to the diameter of the tablecloth. Step 2: State the minimum length. Minimum length = 2.0 m. The minimum length of fabric required is 2.0 m. 1.2.5 Calculate the wastage of fabric per tablecloth if the piece cut is rectangular (length × width). Step 1: Determine the dimensions of the rectangular piece of fabric. To cut a circular tablecloth with a diameter of 2.0 m, the smallest rectangular piece of fabric that can contain it would have a length of 2.0 m and a width of 2.0 m. Step 2: Calculate the area of the rectangular piece of fabric. Area of rectangle = Length × Width = 2.0 m × 2.0 m = 4.0 m^2 Step 3: Recall the area of the tablecloth. From question 1.2.2, the area of one tablecloth is A = (1.0 m)^2 = m^2 ≈ 3.14159 m^2. Step 4: Calculate the wastage of fabric. Wastage = Area of rectangular piece - Area of tablecloth Wastage = 4.0 m^2 - m^2 Wastage ≈ 4.0 m^2 - 3.14159 m^2 Wastage ≈ 0.85841 m^2 The wastage of fabric per tablecloth is approximately 0.86 m^2. 1.2.6 If Madlamini makes 10 tablecloths, calculate the total fabric used in m^2. Step 1: Identify the area of fabric required for one tablecloth. From question 1.2.2, the area of fabric required for one tablecloth is m^2 ≈ 3.14159 m^2. Step 2: Calculate the total fabric used for 10 tablecloths. Total fabric used = Area per tablecloth × Number of tablecloths Total fabric used = m^2 × 10 Total fabric used = 10 m^2 Total fabric used ≈ 10 × 3.14159 m^2 Total fabric used ≈ 31.4159 m^2 The total fabric used for 10 tablecloths is approximately 31.42 m^2. 3 done, 2 left today. You're making progress.