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.
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Problem 15: The tank below was used to harvest water in Embakasi South Constituency. What is the volume of the water tank in cubic metres? Step 1: Identify the dimensions of the rectangular tank from the image. Length (L) = 24 \, m Width (W) = 13 \, m Height (H) = 8 \, m Step 2: Use the formula for the volume of a rectangular prism. V = L × W × H Step 3: Substitute the values and calculate the volume. V = 24 \, m × 13 \, m × 8 \, m V = 312 \, m^2 × 8 \, m V = 2496 \, m^3 The volume of the water tank is 2496 \, m^3. Problem 16: Three bells ring at intervals of 3 minutes, 6 minutes and 9 minutes respectively. After how long will they ring again together? Step 1: To find when the bells will ring together again, calculate the Least Common Multiple (LCM) of their ringing intervals: 3, 6, and 9 minutes. Step 2: Find the prime factorization of each number. 3 = 3^1 6 = 2^1 × 3^1 9 = 3^2 Step 3: Determine the LCM by taking the highest power of all prime factors present. LCM(3, 6, 9) = 2^1 × 3^2 LCM(3, 6, 9) = 2 × 9 LCM(3, 6, 9) = 18 The bells will ring together again after 18 \, minutes. Problem 17: A rectangular garden in the shape below was fenced leaving a pathway. Calculate the shaded area. Step 1: Identify the dimensions of the outer rectangle. Outer Length (L_o) = 15 \, cm Outer Width (W_o) = 13 \, cm Step 2: Calculate the area of the outer rectangle. Area_outer = L_o × W_o Area_outer = 15 \, cm × 13 \, cm Area_outer = 195 \, cm^2 Step 3: Identify the dimensions of the inner (unshaded) rectangle. Inner Length (L_i) = 10 \, cm Inner Width (W_i) = 4 \, cm Step 4: Calculate the area of the inner rectangle. Area_inner = L_i × W_i Area_inner = 10 \, cm × 4 \, cm Area_inner = 40 \, cm^2 Step 5: Calculate the shaded area by subtracting the inner area from the outer area. Shaded Area = Area_outer - Area_inner Shaded Area = 195 \, cm^2 - 40 \, cm^2 Shaded Area = 155 \, cm^2 The shaded area is 155 \, cm^2. That's 2 down. 3 left today — send the next one.