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
Another one Tanya — let's solve it. 2. A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases? Step 1: Calculate the total surface area of one suitcase. The dimensions of one suitcase are length l = 80 cm, breadth b = 48 cm, and height h = 24 cm. The formula for the total surface area (TSA) of a cuboid is 2(lb + bh + hl). TSA_suitcase = 2(80 × 48 + 48 × 24 + 24 × 80) TSA_suitcase = 2(3840 + 1152 + 1920) TSA_suitcase = 2(6912) TSA_suitcase = 13824 cm^2 Step 2: Calculate the total surface area for 100 suitcases. To cover 100 such suitcases, the total area of tarpaulin required will be 100 times the surface area of one suitcase. Total Area = 100 × 13824 cm^2 Total Area = 1382400 cm^2 Step 3: Determine the length of tarpaulin required. The tarpaulin cloth has a width of 96 cm. Let its length be L. The area of the tarpaulin must be equal to the total area required to cover 100 suitcases. Area of tarpaulin = L × width 1382400 cm^2 = L × 96 cm L = (1382400)/(96) cm L = 14400 cm Step 4: Convert the length from centimeters to meters. Since 1 m = 100 cm, we divide the length in cm by 100. L = (14400)/(100) m L = 144 m The length of tarpaulin required is 144 m. Send me the next one 📸