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
You're on a roll — Step 1: Find the surface area of the sphere. Given: Radius (r) = 42 cm Formula for surface area (SA) = 4 r^2 Use = (22)/(7). The final answer must be in square meters. First, convert the radius to meters: r = 42 cm = 0.42 m Substitute the values into the formula: SA = 4 × (22)/(7) × (0.42 m)^2 SA = (88)/(7) × 0.1764 m^2 SA = 12.5714... × 0.1764 m^2 SA = 2.2176 m^2 2.2176 m^2 Step 2: Calculate the volume of the cone. Given: Radius (r) = 10 cm Height (h) = 30 cm Formula for volume (V) = (1)/(3) r^2 h Use = 3.14. Substitute the values into the formula: V = (1)/(3) × 3.14 × (10 cm)^2 × 30 cm V = (1)/(3) × 3.14 × 100 cm^2 × 30 cm V = 3.14 × 100 cm^2 × (30)/(3) cm V = 3.14 × 100 cm^2 × 10 cm V = 3.14 × 1000 cm^3 V = 3140 cm^3 3140 cm^3 Step 3: Find the volume of the cube. Given: Side length (s) = 6sqrt(2) cm The formula for the volume of a cube is V = s^3. Substitute the side length into the formula: V = (6sqrt(2) cm)^3 V = 6^3 × (sqrt(2))^3 cm^3 V = (6 × 6 × 6) × (sqrt(2) × sqrt(2) × sqrt(2)) cm^3 V = 216 × (2 × sqrt(2)) cm^3 V = 216 × 2sqrt(2) cm^3 V = 432sqrt(2) cm^3 432sqrt(2) cm^3 Send me the next one 📸