Your mother wants to renovate her bedroom. You are requested by your mother to supply them with bedroom measurements. You need to assist her with the following items. Measure all the dimensions needed in meters. 1.1 Walls" length, breadth, and height. (6) 12 State the number of windows and measure their length and breadth (give dimensions for each if they are more than one). 13 State the number of doors / openings and measure their leagth and breadth (5) 1.4 Convert the dimensions recorded in QUESTION 1.1 to centimetres and use (10) those values to calculate the volume of the room to the nearest \( \mathrm{cm}^{3} \). 1.5 Calculate the 1.5.1 Area of the walls to be painted in \( \mathrm{m}^{2} \). 1.5.2 Litres of paint needed if two coats are to be applied NB 5 litres of paint covers \( 6 \mathrm{~m}^{2} \) 6 Search for an advertisement of paint and check the price of 20 litre tin and 5 litre tin from your local shops. Use the prices to determine the cheapest tin to buy and mention the name of the shop to buy from. (5) [50]

**Step 1.1: Room Dimensions in Meters** Assume the room has the following dimensions: - Length: \( L = 5\,\text{m} \) - Breadth: \( B = 4\,\text{m} \) - Height: \( H = 3\,\text{m} \) These values represent the dimensions of the walls. --- **Step 1.2: Windows Dimensions** Assume there are 2 windows in the room. Their dimensions are: - Window 1: \( 1.5\,\text{m} \times 1.2\,\text{m} \) - Window 2: \( 1.5\,\text{m} \times 1.2\,\text{m} \) --- **Step 1.3: Doors / Openings Dimensions** Assume there is 1 door in the room. Its dimensions are: - Door: \( 1.0\,\text{m} \times 2.1\,\text{m} \) --- **Step 1.4: Conversion to Centimetres and Volume Calculation** First, convert the room dimensions from metres to centimetres using \[ 1\,\text{m} = 100\,\text{cm} \] Thus, \[ L = 5\,\text{m} = 500\,\text{cm}, \quad B = 4\,\text{m} = 400\,\text{cm}, \quad H = 3\,\text{m} = 300\,\text{cm} \] The volume \( V \) of the room in cubic centimetres is calculated by \[ V = L \times B \times H = 500\,\text{cm} \times 400\,\text{cm} \times 300\,\text{cm} \] \[ V = 60\,000\,000\,\text{cm}^{3} \] So, the room's volume is \( 60\,000\,000\,\text{cm}^{3} \). --- **Step 1.5.1: Area of the Walls to be Painted** 1. **Calculate Total Wall Area** For a rectangular room, the total area of the four walls is given by: \[ \text{Total Wall Area} = 2(L \times H) + 2(B \times H) \] Substitute the given dimensions (in metres): \[ \text{Total Wall Area} = 2(5 \times 3) + 2(4 \times 3) = 2(15) + 2(12) = 30 + 24 = 54\,\text{m}^{2} \] 2. **Subtract the Areas of the Windows and the Door** - Total window area: Each window has an area of \[ 1.5\,\text{m} \times 1.2\,\text{m} = 1.8\,\text{m}^{2} \] For 2 windows: \[ 2 \times 1.8\,\text{m}^{2} = 3.6\,\text{m}^{2} \] - Door area: \[ 1.0\,\text{m} \times 2.1\,\text{m} = 2.1\,\text{m}^{2} \] Thus, the paintable wall area is: \[ \text{Paintable Wall Area} = 54\,\text{m}^{2} - 3.6\,\text{m}^{2} - 2.1\,\text{m}^{2} = 48.3\,\text{m}^{2} \] --- **Step 1.5.2: Calculation of Litres of Paint Needed** Since two coats are to be applied, the total area to be painted becomes: \[ \text{Total Painted Area} = 48.3\,\text{m}^{2} \times 2 = 96.6\,\text{m}^{2} \] Given that 5 litres of paint cover \( 6\,\text{m}^{2} \), the required amount of paint in litres is calculated as: \[ \text{Litres of Paint} = \frac{96.6\,\text{m}^{2}}{6\,\text{m}^{2}/5\,\text{litres}} = \frac{96.6}{6} \times 5 \] \[ \frac{96.6}{6} \approx 16.1 \quad \Longrightarrow \quad 16.1 \times 5 \approx 80.5\,\text{litres} \] Rounding to the nearest litre, approximately 81 litres of paint are needed. --- **Step 1.6: Advertisement and Price Comparison** Assume the following prices are obtained from local shops: - A 20-litre tin of paint costs \$100. - A 5-litre tin of paint costs \$30. Calculate the cost per litre for each tin: 1. For the 20-litre tin: \[ \text{Cost per litre} = \frac{\$100}{20\,\text{litres}} = \$5\,\text{per litre} \] 2. For the 5-litre tin: \[ \text{Cost per litre} = \frac{\$30}{5\,\text{litres}} = \$6\,\text{per litre} \] Since \$5 per litre is less than \$6 per litre, the 20-litre tin is the cheaper option. **Decision:** Buy the 20-litre tin at \$100 from **ABC Paints** (assumed shop name). --- **Summary of Answers** 1. Room dimensions: \( L = 5\,\text{m},\quad B = 4\,\text{m},\quad H = 3\,\text{m} \) 2. Windows: 2 windows, each \( 1.5\,\text{m} \times 1.2\,\text{m} \) 3. Door: 1 door, \( 1.0\,\text{m} \times 2.1\,\text{m} \) 4. Volume of the room: \( 60\,000\,000\,\text{cm}^{3} \) 5. Paintable wall area: \( 48.3\,\text{m}^{2} \); after applying two coats, a total area of \( 96.6\,\text{m}^{2} \) needs painting Paint required: approximately 81 litres. 6. Cheapest tin: A 20-litre tin at \$100 from **ABC Paints** is the cheapest option.