Convert 500 cm to m. Calculate the area of one window (L=1.2m, B=0.6m). Calculate the area of the vent (diameter=0.5m, area=2pir2, pi=3.142). Calculate the area of the rectangular wall (L=5m, B=2.6m).

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Asked on May 8, 2026Mathematics

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.

Accepted Answer · 2026-05-08T02:49:35.888Z

Here are the solutions to the questions: 1. Convert 500 cm to m. Step 1: To convert centimeters to meters, divide by 100. 500 cm = (500)/(100) m 500 cm = 5 m 2. Calculate the area of one window. Step 1: Identify the dimensions of one window from the diagram: length (L) = 1.2 m, breadth (B) = 0.6 m. Step 2: Use the formula for the area of a rectangle, Area = L × B. Area_window = 1.2 m × 0.6 m Area_window = 0.72 m^2 3. Calculate the area of the vent. Step 1: Identify the diameter of the circular vent from the diagram: 0.5 m. Calculate the radius (r). r = 0.5 m2 = 0.25 m Step 2: Use the given formula for the area of the vent, Area = 2 r^2, with = 3.142. Area_vent = 2 × 3.142 × (0.25 m)^2 Area_vent = 2 × 3.142 × 0.0625 m^2 Area_vent = 0.39275 m^2 4. Calculate the area of the rectangular part of the wall. Step 1: Identify the dimensions of the rectangular wall: length (L) = 5 m (from Q1), breadth (B) = 2.6 m. Step 2: Use the formula for the area of a rectangle, Area = L × B. Area_rectangular\_wall = 5 m × 2.6 m Area_rectangular\_wall = 13 m^2 5. Calculate the area of the gable. Step 1: Identify the dimensions of the triangular gable: base (b) = 5 m, height (h) = 1.8 m. Step 2: Use the formula for the area of a triangle, Area = (1)/(2) × b × h. Area_gable = (1)/(2) × 5 m × 1.8 m Area_gable = 2.5 m × 1.8 m Area_gable = 4.5 m^2 6. Prudence states that the area of the Wall that must be painted is 14.42 m². Is this statement valid? Set your work out clearly. (PLEASE NOTE THAT THE VENT AND THE WINDOWS WILL NOT BE PAINTED) Step 1: Calculate the total area of the front wall (rectangular part + gable). Total\_wall\_area = Area_rectangular\_wall + Area_gable Total\_wall\_area = 13 m^2 + 4.5 m^2 Total\_wall\_area = 17.5 m^2 Step 2: Calculate the total area of the four windows. Area_4\_windows = 4 × Area_window Area_4\_windows = 4 × 0.72 m^2 Area_4\_windows = 2.88 m^2 Step 3: Calculate the area to be painted by subtracting the areas of the windows and the vent from the total wall area. Area_painted = Total\_wall\_area - Area_4\_windows - Area_vent Area_painted = 17.5 m^2 - 2.88 m^2 - 0.39275 m^2 Area_painted = 14.62

Accepted Answer · 2026-05-08T02:49:35.888Z

Here are the solutions to the questions: 1. Convert 500 cm to m. Step 1: To convert centimeters to meters, divide by 100. 500 cm = (500)/(100) m 500 cm = 5 m 2. Calculate the area of one window. Step 1: Identify the dimensions of one window from the diagram: length (L) = 1.2 m, breadth (B) = 0.6 m. Step 2: Use the formula for the area of a rectangle, Area = L × B. Area_window = 1.2 m × 0.6 m Area_window = 0.72 m^2 3. Calculate the area of the vent. Step 1: Identify the diameter of the circular vent from the diagram: 0.5 m. Calculate the radius (r). r = 0.5 m2 = 0.25 m Step 2: Use the given formula for the area of the vent, Area = 2 r^2, with = 3.142. Area_vent = 2 × 3.142 × (0.25 m)^2 Area_vent = 2 × 3.142 × 0.0625 m^2 Area_vent = 0.39275 m^2 4. Calculate the area of the rectangular part of the wall. Step 1: Identify the dimensions of the rectangular wall: length (L) = 5 m (from Q1), breadth (B) = 2.6 m. Step 2: Use the formula for the area of a rectangle, Area = L × B. Area_rectangular\_wall = 5 m × 2.6 m Area_rectangular\_wall = 13 m^2 5. Calculate the area of the gable. Step 1: Identify the dimensions of the triangular gable: base (b) = 5 m, height (h) = 1.8 m. Step 2: Use the formula for the area of a triangle, Area = (1)/(2) × b × h. Area_gable = (1)/(2) × 5 m × 1.8 m Area_gable = 2.5 m × 1.8 m Area_gable = 4.5 m^2 6. Prudence states that the area of the Wall that must be painted is 14.42 m². Is this statement valid? Set your work out clearly. (PLEASE NOTE THAT THE VENT AND THE WINDOWS WILL NOT BE PAINTED) Step 1: Calculate the total area of the front wall (rectangular part + gable). Total\_wall\_area = Area_rectangular\_wall + Area_gable Total\_wall\_area = 13 m^2 + 4.5 m^2 Total\_wall\_area = 17.5 m^2 Step 2: Calculate the total area of the four windows. Area_4\_windows = 4 × Area_window Area_4\_windows = 4 × 0.72 m^2 Area_4\_windows = 2.88 m^2 Step 3: Calculate the area to be painted by subtracting the areas of the windows and the vent from the total wall area. Area_painted = Total\_wall\_area - Area_4\_windows - Area_vent Area_painted = 17.5 m^2 - 2.88 m^2 - 0.39275 m^2 Area_painted = 14.62

Convert 500 cm to m. Calculate the area of one window (L=1.2m, B=0.6m). Calculate the area of the vent (diameter=0.5m, area=2pir2, pi=3.142). Calculate the area of the rectangular wall (L=5m, B=2.6m).

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Convert 500 cm to m. Calculate the area of one window (L=1.2m, B=0.6m). Calculate the area of the vent (diameter=0.5m, area=2pir2, pi=3.142). Calculate the area of the rectangular wall (L=5m, B=2.6m).

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