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: Calculate the area of the cross-section. The cross-section is an equilateral triangle ABC with side length s = 4 cm. The formula for the area of an equilateral triangle is sqrt(3)4s^2. Area of cross-section = sqrt(3)4(4^2) Area of cross-section = sqrt(3)4(16) Area of cross-section = 4sqrt(3) cm^2 Step 2: Identify the length of the prism. The length of the prism is given as CD = AE = BF = 6 cm. Length of prism = 6 cm Step 3: Calculate the volume of the prism. The volume of a prism is given by the formula: Volume = Area of cross-section × Length. Volume = (4sqrt(3) cm^2) × (6 cm) Volume = 24sqrt(3) cm^3 Now, we calculate the numerical value and round to 1 decimal place. Using sqrt(3) ≈ 1.73205: Volume ≈ 24 × 1.73205 Volume ≈ 41.5692 cm^3 Rounding to 1 decimal place: Volume ≈ 41.6 cm^3 The volume of the prism is 41.6 cm^3. That's 2 down. 3 left today — send the next one.