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
i) For a cube with edge length a = 7 m: Step 1: Calculate the Volume (V). The formula for the volume of a cube is V = a^3. V = (7 m)^3 V = 7 m × 7 m × 7 m V = 343 m^3 Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is LSA = 4a^2. LSA = 4 × (7 m)^2 LSA = 4 × 49 m^2 LSA = 196 m^2 Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is TSA = 6a^2. TSA = 6 × (7 m)^2 TSA = 6 × 49 m^2 TSA = 294 m^2 For a = 7 m: Volume: 343 m^3 Lateral Surface Area: 196 m^2 Total Surface Area: 294 m^2 ii) For a cube with edge length a = 5.6 cm: Step 1: Calculate the Volume (V). The formula for the volume of a cube is V = a^3. V = (5.6 cm)^3 V = 5.6 cm × 5.6 cm × 5.6 cm V = 175.616 cm^3 Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is LSA = 4a^2. LSA = 4 × (5.6 cm)^2 LSA = 4 × 31.36 cm^2 LSA = 125.44 cm^2 Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is TSA = 6a^2. TSA = 6 × (5.6 cm)^2 TSA = 6 × 31.36 cm^2 TSA = 188.16 cm^2 For a = 5.6 cm: Volume: 175.616 cm^3 Lateral Surface Area: 125.44 cm^2 Total Surface Area: 188.16 cm^2