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
Here's how to solve the problem: a) Find the value of y. Step 1: Identify the dimensions of the cuboid. From the diagram, the length is y+4 cm, the height is y+2 cm. The width (or depth) of the cuboid is labeled with two expressions: 2y+1 cm and y+1 cm. Since these represent the same physical dimension, they must be equal. Step 2: Set up an equation using the expressions for the width. 2y+1 = y+1 Step 3: Solve the equation for y. Subtract y from both sides: 2y - y + 1 = 1 y + 1 = 1 Subtract 1 from both sides: y = 1 - 1 y = 0 The value of y is: y = 0 b) Calculate its volume. Step 1: Determine the actual dimensions of the cuboid using y=0. Length (l) = y+4 = 0+4 = 4 cm Width (w) = 2y+1 = 2(0)+1 = 1 cm (or y+1 = 0+1 = 1 cm) Height (h) = y+2 = 0+2 = 2 cm Step 2: State the formula for the volume of a cuboid. V = l × w × h Step 3: Substitute the dimensions into the formula and calculate the volume. V = 4 cm × 1 cm × 2 cm V = 8 cm^3 The volume of the cuboid is: 8 cm^3 That's 2 down. 3 left today — send the next one.