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.
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Here are the calculations for the volume and surface area of the cylinder. The dimensions of the cylinder are: • Height (h) = 10 dm • Radius (r) = 4 cm Step 1: Convert all dimensions to a consistent unit. We will convert decimeters to centimeters, as the radius is given in centimeters. 1 dm = 10 cm h = 10 dm × 10 cm1 dm = 100 cm So, the height is 100 cm and the radius is 4 cm. Step 2: Calculate the volume of the cylinder. The formula for the volume of a cylinder is V = r^2 h. V = (4 cm)^2 (100 cm) V = (16 cm^2) (100 cm) V = 1600 cm^3 Using ≈ 3.14159: V ≈ 1600 × 3.14159 cm^3 V ≈ 5026.55 cm^3 The volume of the cylinder is 5026.55 cm^3. Step 3: Calculate the surface area of the cylinder. The formula for the total surface area of a cylinder is SA = 2 r^2 + 2 r h. SA = 2 (4 cm)^2 + 2 (4 cm) (100 cm) SA = 2 (16 cm^2) + 2 (400 cm^2) SA = 32 cm^2 + 800 cm^2 SA = 832 cm^2 Using ≈ 3.14159: SA ≈ 832 × 3.14159 cm^2 SA ≈ 2613.81 cm^2 The surface area of the cylinder is 2613.81 cm^2. That's 2 down. 3 left today — send the next one.