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: Understand the problem and the formula for percentage increase in volume. The length, breadth, and height of a cuboid are increased by x\%, y\%, and z\% respectively. The percentage increase in volume can be calculated using the formula: Percentage increase = (x + y + z + (xy + yz + zx)/(100) + (xyz)/(10000))\% Given increases are: x = 20\% y = 25\% z = 40\% Step 2: Substitute the values into the formula. Percentage increase = (20 + 25 + 40 + ((20 × 25) + (25 × 40) + (40 × 20))/(100) + (20 × 25 × 40)/(10000))\% Step 3: Calculate the sum of individual increases. 20 + 25 + 40 = 85 Step 4: Calculate the sum of products of two dimensions, divided by 100. ((20 × 25) + (25 × 40) + (40 × 20))/(100) = (500 + 1000 + 800)/(100) = (2300)/(100) = 23 Step 5: Calculate the product of three dimensions, divided by 10000. (20 × 25 × 40)/(10000) = (500 × 40)/(10000) = (20000)/(10000) = 2 Step 6: Add all the calculated parts to find the total percentage increase. Percentage increase = 85 + 23 + 2 = 110\% The percentage increase in the volume of the cuboid is 110%. This matches option a. The final answer is a. 110\%. 3 done, 2 left today. You're making progress.