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
Mimi, let's knock this out. Activity 24 24.2.1 Calculate the diameter of the tablecloth to be cut from the material, including the additional centimetres for the hem. Step 1: Identify the given dimensions. The diameter of the table is 130 cm. The additional length for the hem on each side is 25 cm. Step 2: Calculate the total diameter of the tablecloth. The total diameter will be the table's diameter plus the hem allowance on both sides. Diameter = 130 cm + 25 cm + 25 cm Diameter = 180 cm Step 3: Convert the diameter to meters for consistency with later calculations. Diameter = 180 cm × 1 m100 cm Diameter = 1.8 m The diameter of the tablecloth is 1.8 m. 24.2.2 Calculate the area (in m²) of the tablecloth material. You may use the formula: Area = Side × Side Step 1: Identify the side length of the material. The material size is 2.3 m. Assuming it's a square, the side length is 2.3 m. Step 2: Calculate the area using the given formula. Area of material = Side × Side Area of material = 2.3 m × 2.3 m Area of material = 5.29 m^2 The area of the tablecloth material is 5.29 m^2. 24.2.3 Calculate the area (in m²) of the tablecloth that was cut from the material. You may use the following formula: Area = (radius)^2, where = 3.142 Step 1: Determine the radius of the tablecloth. From 24.2.1, the diameter of the tablecloth is 1.8 m. Radius = Diameter2 Radius = 1.8 m2 Radius = 0.9 m Step 2: Calculate the area using the given formula and = 3.142. Area of tablecloth = (radius)^2 Area of tablecloth = 3.142 × (0.9 m)^2 Area of tablecloth = 3.142 × 0.81 m^2 Area of tablecloth = 2.54502 m^2 The area of the tablecloth is 2.54502 m^2. 24.2.4 Calculate how much material was wasted when the table cloth was cut. You may use the formula: Wasted material = Area of a material - Area of tablecloth Step 1: Use the areas calculated in 24.2.2 and 24.2.3. Area of material = 5.29 m^2 Area of tablecloth = 2.54502 m^2 Step 2: Calculate the wasted material. Wasted material = 5.29 m^2 - 2.54502 m^2 Wasted material = 2.74498 m^2 The amount of material wasted is 2.74498 m^2. Send me the next one 📸