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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Morning Boipelo — let's get this done. Here are the solutions to the questions: 3.1 Determine the radius of the can, in cm. Step 1: Identify the given diameter and convert it to centimeters. The diameter of the can is given as 55 mm. Since 1 cm = 10 mm, we convert the diameter to centimeters: Diameter = 55 mm × 1 cm10 mm = 5.5 cm Step 2: Calculate the radius using the diameter. The radius is half of the diameter. Radius = Diameter2 = 5.5 cm2 = 2.75 cm The radius of the can is 2.75 cm. 3.2 Calculate the total surface area of the can, rounded to the nearest cm², if the radius of the can is rounded to 3 cm. Step 1: Identify the given values for radius, height, and . For this calculation, the radius is given as 3 cm. The height of the can is 16 cm. The value of is given as 3.142. Step 2: Use the formula for the surface area of a cylinder. The formula for the surface area of a cylinder is: Surface area = 2 × × radius^2 + 2 × × radius × height Step 3: Substitute the values into the formula and calculate. Surface area = (2 × 3.142 × (3 cm)^2) + (2 × 3.142 × 3 cm × 16 cm) Surface area = (2 × 3.142 × 9 cm^2) + (2 × 3.142 × 48 cm^2) Surface area = 56.556 cm^2 + 301.632 cm^2 Surface area = 358.188 cm^2 Step 4: Round the surface area to the nearest cm². Surface area ≈ 358 cm^2 The total surface area of the can, rounded to the nearest cm², is 358 cm^2. 3.3 The area of the label of the can covers 35% of the total surface area of the can. Calculate the total area covered by the label of the can. Step 1: Identify the total surface area from the previous calculation and the percentage covered by the label. Total surface area = 358 cm^2 (from question 3.2). Percentage covered by the label = 35\%. Step 2: Calculate the area covered by the label. Label area = 35\% of 358 cm^2 Label area = 0.35 × 358 cm^2 Label area = 125.3 cm^2 The total area covered by the label of the can is 125.3 cm^2. Send me the next one 📸