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
Hey Mimi, good to see you again. 24.1.1 Step 1: Identify the dimensions of the box. The length of the box is L = 28 cm. The width of the box is W = 15 cm. The height of the box is H = 8 cm. Step 2: Use the formula for the volume of a rectangular prism. V = L × W × H Step 3: Substitute the values and calculate the volume. V = 28 cm × 15 cm × 8 cm V = 420 cm^2 × 8 cm V = 3360 cm^3 The volume of the box is 3360 cm^3. 24.1.2 Step 1: Calculate the volume of one chocolate bar. The box packs 84 rectangular chocolate bars. The total volume of the chocolate bars is the volume of the box. V_chocolate = Volume of boxNumber of chocolate bars V_chocolate = 3360 cm^384 V_chocolate = 40 cm^3 Step 2: Identify the given area of the base of a chocolate bar. Area of base = 35 cm^2. Step 3: Use the formula Volume = area of base × thickness to find the thickness. V_chocolate = Area of base × thickness 40 cm^3 = 35 cm^2 × thickness thickness = 40 cm^335 cm^2 thickness = (8)/(7) cm thickness ≈ 1.14 cm The thickness of a chocolate bar is (8)/(7) cm ≈ 1.14 cm. 24.2 This question asks about the dimensions for a circular tablecloth and the available square material. I will calculate the required diameter of the tablecloth. Step 1: Identify the diameter of the table. Diameter of table = 130 cm. Step 2: Calculate the diameter of the tablecloth needed to cover the table and hang over. The tablecloth hangs 25 cm over the edge on all sides. D_no hem = Diameter of table + 2 × Overhang D_no hem = 130 cm + 2 × 25 cm D_no hem = 130 cm + 50 cm D_no hem = 180 cm Step 3: Calculate the total diameter of the tablecloth needed, including the hem. A hem of 1.8 cm is added right around. This means 1.8 cm is added to the radius on all sides, so 2 × 1.8 cm is added to the diameter. D_required = D_no hem + 2 × Hem allowance D_required = 180 cm + 2 × 1.8 cm D_required = 180 cm + 3.6 cm D_required = 183.6 cm Step 4: State the dimensions of the available material. The tablecloth material is square with a side length of 2.3 m. Convert meters to centimeters: Side length of material = 2.3 m × 100 cm/m = 230 cm. The required diameter for the circular tablecloth is 183.6 cm. The available square material has a side length of 230 cm. Send me the next one 📸