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: Identify the given dimensions of the cylinder. The radius of the cylinder is r = 7 cm. The height of the cylinder is h = 10 cm. Step 2: Write down the formula for the total surface area of a cylinder. The total surface area (A) of a cylinder is given by the formula: A = 2 r^2 + 2 rh where 2 r^2 is the area of the two circular bases and 2 rh is the lateral surface area. Step 3: Substitute the given values into the formula. Using = (22)/(7): A = 2 × (22)/(7) × (7 cm)^2 + 2 × (22)/(7) × 7 cm × 10 cm Step 4: Calculate the area of the bases. 2 r^2 = 2 × (22)/(7) × 49 cm^2 2 r^2 = 2 × 22 × 7 cm^2 2 r^2 = 308 cm^2 Step 5: Calculate the lateral surface area. 2 rh = 2 × (22)/(7) × 7 cm × 10 cm 2 rh = 2 × 22 × 10 cm^2 2 rh = 440 cm^2 Step 6: Add the areas to find the total surface area. A = 308 cm^2 + 440 cm^2 A = 748 cm^2 The total surface area of the object is 748 cm^2. Send me the next one 📸