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 Volume of the cuboid. The dimensions are: Length (l) = 22 cm Breadth (b) = 12 cm Height (h) = 7.5 cm The formula for the volume of a cuboid is V = l × b × h. V = 22 cm × 12 cm × 7.5 cm V = 264 cm^2 × 7.5 cm V = 1980 cm^3 Step 2: Calculate the Lateral Surface Area (LSA) of the cuboid. The formula for the lateral surface area of a cuboid is LSA = 2h(l+b). LSA = 2 × 7.5 cm × (22 cm + 12 cm) LSA = 15 cm × (34 cm) LSA = 510 cm^2 Step 3: Calculate the Total Surface Area (TSA) of the cuboid. The formula for the total surface area of a cuboid is TSA = 2(lb + bh + hl). TSA = 2((22 cm × 12 cm) + (12 cm × 7.5 cm) + (7.5 cm × 22 cm)) TSA = 2(264 cm^2 + 90 cm^2 + 165 cm^2) TSA = 2(519 cm^2) TSA = 1038 cm^2 The volume, lateral surface area, and total surface area for the given dimensions are: Volume: 1980 cm^3 Lateral Surface Area: 510 cm^2 Total Surface Area: 1038 cm^2