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
Here are the solutions to the problems: 8. A cube has all sides of length 2 cm. What will be the area of the hexagon be, if it is enlarged with scale factor 3? This question appears to have a slight mix-up in wording, referring to a cube but then asking about a hexagon. Based on the image, we will find the area of the enlarged hexagon. Step 1: Identify the original area and the scale factor. Original area of the hexagon = 60 cm^2. Scale factor k = 3. Step 2: Use the relationship between scale factor and area. If a figure is enlarged by a scale factor k, its area is enlarged by a factor of k^2. New Area = Original Area × k^2 New Area = 60 cm^2 × (3)^2 New Area = 60 cm^2 × 9 New Area = 540 cm^2 The area of the enlarged hexagon will be 540 cm^2. 9. What scale factor is needed to enlarge the smaller cuboid to become larger? To find the scale factor, we compare the lengths of corresponding sides of the two cuboids. Step 1: Identify corresponding dimensions. Smaller cuboid dimensions: Length = 4 cm, Width = 3 cm, Height = 2 cm. Larger cuboid dimensions: Length = 8 cm, Width = 6 cm, Height = 4 cm. Step 2: Calculate the ratio of corresponding dimensions (Larger to Smaller). Ratio of lengths: 8 cm4 cm = 2 Ratio of widths: 6 cm3 cm = 2 Ratio of heights: 4 cm2 cm = 2 Since all ratios are equal, the scale factor is 2. The scale factor is 2.