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 are the volumes of the given shapes: Shape A: Hexagonal Prism Assumption: The base is a regular hexagon with a side length of 25 cm. Step 1: Identify the dimensions and formula. The side length of the regular hexagonal base is s = 25 cm. The height of the prism is h = 10 cm. The area of a regular hexagon is A = 3sqrt(3)2 s^2. The volume of a prism is V = A × h. Step 2: Calculate the area of the hexagonal base. A = 3sqrt(3)2 (25 cm)^2 A = 3sqrt(3)2 (625 cm^2) A = 1875sqrt(3)2 cm^2 Step 3: Calculate the volume of the hexagonal prism. V_A = (1875sqrt(3)2 cm^2) × (10 cm) V_A = 9375sqrt(3) cm^3 Using sqrt(3) ≈ 1.73205: V_A ≈ 9375 × 1.73205 cm^3 V_A ≈ 16237.97 cm^