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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1.2.1) Calculate the radius of the cylindrical magic cube if the diameter is 67 mm. Step 1: Recall the relationship between diameter and radius. The radius is half of the diameter. Radius = Diameter2 Step 2: Substitute the given diameter and calculate the radius. Radius = 67 mm2 Radius = 33.5 mm The radius of the cylindrical magic cube is 33.5 mm. 1.2.2) Calculate the total volume of the cylindrical magic cube in mm^3. The following formula may be used: Volume of cylinder = × radius × radius × height, where = 3.142. Step 1: Identify the given dimensions and value. From the image, the height of the cylindrical magic cube is 60 mm. From 1.2.1, the radius is 33.5 mm. The value of is given as 3.142. Step 2: Substitute the values into the volume formula. Volume = × radius^2 × height Volume = 3.142 × (33.5 mm)^2 × 60 mm Volume = 3.142 × 1122.25 mm^2 × 60 mm Volume = 3.142 × 67335 mm^3 Volume = 211516.47 mm^3 The total volume of the cylindrical magic cube is 211516.47 mm^3. 1.2.3) Calculate the total surface area of the magic cube in mm^2. The following formula may be used: Total surface area = side × side × 6 Step 1: Identify the side length of the cubic magic cube. From the image, the side length of the cubic magic cube is 57 mm. Step 2: Substitute the side length into the surface area formula. Total surface area = side^2 × 6 Total surface area = (57 mm)^2 × 6 Total surface area = 3249 mm^2 × 6 Total surface area = 19494 mm^2 The total surface area of the magic cube is 19494 mm^2. That's 2 down. 3 left today — send the next one.