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
Step 1: Convert all dimensions to a consistent unit, centimeters (cm). Given dimensions of one brick: Length (l_b) = 25 cm Width (w_b) = 10 cm Height (h_b) = 8 cm Given dimensions of the wall: Length (L_w) = 9.9 m = 9.9 × 100 cm = 990 cm Thickness (W_w) = 20 cm Height (H_w) = 30 cm Step 2: Calculate the volume of one brick. The volume of a brick (V_b) is given by the product of its length, width, and height. V_b = l_b × w_b × h_b V_b = 25 cm × 10 cm × 8 cm V_b = 2000 cm^3 Step 3: Calculate the total volume of the wall. The volume of the wall (V_w) is given by the product of its length, thickness, and height. V_w = L_w × W_w × H_w V_w = 990 cm × 20 cm × 30 cm V_w = 594000 cm^3 Step 4: Calculate the volume occupied by bricks in the wall. The problem states that 10\% of the wall's volume is filled with cement (mortar). This means the remaining 90\% of the wall's volume is occupied by bricks. Volume occupied by bricks (V_bricks\_in\_wall) = 90\% of V_w V_bricks\_in\_wall = 0.90 × V_w V_bricks\_in\_wall = 0.90 × 594000 cm^3 V_bricks\_in\_wall = 534600 cm^3 Step 5: Calculate the number of bricks required. The number of bricks (N) is the total volume occupied by bricks in the wall divided by the volume of one brick. N = V_bricks\_in\_wallV_b N = 534600 cm^32000 cm^3 N = 267.3 The number of bricks required is 267.3. Drop the next question! 📸