Construct a diagonal scale of 30mm = 1km to read up to 6km in divisions of 100m.

Here are the answers to your questions: 5. Construct a diagonal scale of 30mm = 1km to read up to 6km in divisions of 10m. Step 1: Calculate the Representative Fraction (RF). RF = Drawing lengthActual length = 30mm1km = 30mm1 × 1000 × 1000mm = (30)/(1,000,000) = (3)/(100,000) Step 2: Calculate the total length of the scale. The scale needs to read up to 6km. Total length = RF × Maximum length = (3)/(100,000) × 6km = (3)/(100,000) × (6 × 1000 × 1000mm) = 180mm Step 3: Construct the main scale. 1. Draw a line 180mm long. 2. Divide this line into 6 equal primary divisions, each representing 1km (each division will be 30mm long). 3. Label the divisions 0, 1, 2, 3, 4, 5km from left to right, starting with 0 at the first mark. The leftmost division (from 0 to the left) will be used for subdivisions. Step 4: Subdivide the leftmost primary division (for 100m divisions). 1. The leftmost division represents 1km (1000m). 2. Divide this 30mm segment into 10 equal parts. Each part will represent 100m. 3. Label these subdivisions 0, 100, 200, , 900m from right to left. Step 5: Construct the diagonal part (for 10m divisions). 1. Draw a vertical line upwards from the 0 mark on the main scale. 2. Draw 10 equally spaced horizontal lines above the main scale, parallel to it. 3. From the 0 mark on the main scale, draw a diagonal line to the 10th mark on the vertical line at the 1km mark (the left end of the first primary division). 4. From each 100m subdivision mark (left of 0), draw vertical lines upwards to the top horizontal line. 5. The intersection of these vertical lines with the diagonal lines will allow reading of 10m divisions. Indicate the following readings: i) 5.81km: Locate 5km on the main scale. Move left to the 800m mark on the main subdivision. Then, move up along the vertical line from 800m to the 1st diagonal line (representing 10m). ii) 2.53km: Locate 2km on the main scale. Move left to the 500m mark on the main subdivision. Then, move up along the vertical line from 500m to the 3rd diagonal line (representing 30m). iii) 4.67km: Locate 4km on the main scale. Move left to the 600m mark on the main subdivision. Then, move up along the vertical line from 600m to the 7th diagonal line (representing 70m). 6. Construct a plain scale of 30mm represents 1m to read up to 5m in intervals of 100mm. Step 1: Calculate the Representative Fraction (RF). RF = Drawing lengthActual length = 30mm1m = 30mm1000mm = (3)/(100) Step 2: Calculate the total length of the scale. The scale needs to read up to 5m. Total length = RF × Maximum length = (3)/(100) × 5m = (3)/(100) × (5 × 1000mm) = 150mm Step 3: Construct the main scale. 1. Draw a line 150mm long. 2. Divide this line into 5 equal primary divisions, each representing 1m (each division will be 30mm long). 3. Label the divisions 0, 1, 2, 3, 4m from left to right, starting with 0 at the first mark. The leftmost division (from 0 to the left) will be used for subdivisions. Step 4: Subdivide the leftmost primary division (for 100mm divisions). 1. The leftmost division represents 1m (1000mm). 2. Divide this 30mm segment into 10 equal parts. Each part will represent 100mm (or 0.1m). 3. Label these subdivisions 0, 100, 200, , 900mm (or 0.1, 0.2, , 0.9m) from right to left. Indicate the following readings: i) 2.5m: Locate 2m on the main scale. Move left to the 500mm (or 0.5m) mark on the subdivision. ii) 4.5m: Locate 4m on the main scale. Move left to